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John 3:14-16 (ESV):
14 And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, 15 that whoever believes in him may have eternal life. 16 “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.
Related: What exactly does it mean for a soul to be destroyed in gehenna? Matthew 10:28
What does "perish" mean in this context?
"Perish" is described as the fate opposite "eternal life".
Eternal life is defined by Jesus:
And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent.
To perish would then be (or at the very least include) not knowing God. I make the case in this post that eternal life is as described by Dr. Jason Carroll:
Eternal life is a life that is both endless in duration and godlike in quality
The opposite end of the spectrum is directly described by Paul:
Such people will suffer the punishment of eternal destruction by being separated from the Lord's presence and from his glorious power (2 Thess 1:9)
The penalty of eternal destruction is to be separated from God.
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When does that happen?
Permanent separation from God is the second death, described as coming after judgment (see Rev. 20:12-15).
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How long does it take for a person to "perish"?
We are not told (note that annihilationism does not have an answer to this question either).
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Conclusion
This verse is unlikely to move the needle either way in a discussion of annihilationism--the juxtaposition of life & death is to be found in many passages of scripture, not just this one.
Those who see the second death as annihilation will read John 3:16 this way as well; those who see death as a separation will read John 3:16 that way as well.
Your first question is, "What does "perish" mean in this context?" While the answers already presented are pretty good, they don't effectively answer what "perish" means in this context, as they forget to take some essential parts of the context into account, namely the two preceding verses(14 and 15). Once we take those into consideration, everything falls into place quite effortlessly. Let us, however, first do a word study. What do the words "perish" and "eternal life" mean?
John 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth on him should not perish, but have eternal life. (ASV)
The word for "perish" in John 3:16 is ἀπόληται, pronounced apolētai. It is a form of the verb ἀπόλλυμι(Strong's G622), pronounced apollumi. It's primarily used to refer to the end of life, i.e. death, but it can be used in other ways as well. It appears 92 times in the New Testament, and for our purposes, we will take a look at each occurrence. The words in bold are all translated from the Greek word ἀπόλλυμι(all of the following are taken from Young's Literal Translation).
Matthew 2:13 And on their having withdrawn, lo, a messenger of the Lord doth appear in a dream to Joseph, saying, 'Having risen, take the child and his mother, and flee to Egypt, and be thou there till I may speak to thee, for Herod is about to seek the child to destroy him.'
Matthew 5:29-30 'But, if thy right eye doth cause thee to stumble, pluck it out and cast from thee, for it is good to thee that one of thy members may perish, and not thy whole body be cast to gehenna. 30 And, if thy right hand doth cause thee to stumble, cut it off, and cast from thee, for it is good to thee that one of thy members may perish, and not thy whole body be cast to gehenna.
Matthew 8:25 and his disciples having come to him, awoke him, saying, 'Sir, save us; we are perishing.'
Matthew 9:17 'Nor do they put new wine into old skins, and if not--the skins burst, and the wine doth run out, and the skins are destroyed, but they put new wine into new skins, and both are preserved together.'
Matthew 10:6; 28; 39; 42 and be going rather unto the lost sheep of the house of Israel.; And be not afraid of those killing the body, and are not able to kill the soul, but fear rather Him who is able both soul and body to destroy in gehenna.; He who found his life shall lose it, and he who lost his life for my sake shall find it.; and whoever may give to drink to one of these little ones a cup of cold water only in the name of a disciple, verily I say to you, he may not lose his reward.'
Matthew 12:14 And the Pharisees having gone forth, held a consultation against him, how they might destroy him,
Matthew 15:24 and he answering said, 'I was not sent except to the lost sheep of the house of Israel.'
Matthew 16:25 for whoever may will to save his life, shall lose it, and whoever may lose his life for my sake shall find it,
Matthew 18:14 so it is not will in presence of your Father who is in the heavens, that one of these little ones may perish.
Matthew 21:41 They say to him, 'Evil men--he will evilly destroy them, and the vineyard will give out to other husbandmen, who will give back to him the fruits in their seasons.'
Matthew 22:7 And the king having heard, was wroth, and having sent forth his soldiers, he destroyed those murderers, and their city he set on fire;
Matthew 26:52 Then saith Jesus to him, 'Turn back thy sword to its place; for all who did take the sword, by the sword shall perish;
Matthew 27:20 And the chief priests and the elders did persuade the multitudes that they might ask for themselves Barabbas, and might destroy Jesus;
Mark 1:24 saying, 'Away! what--to us and to thee, Jesus the Nazarene? thou didst come to destroy us; I have known thee who thou art--the Holy One of God.'
Mark 2:22 and no one doth put new wine into old skins, and if not--the new wine doth burst the skins, and the wine is poured out, and the skins will be destroyed; but new wine into new skins is to be put.'
Mark 3:6 and the Pharisees having gone forth, immediately, with the Herodians, were taking counsel against him how they might destroy him.
Mark 4:38 and he himself was upon the stern, upon the pillow sleeping, and they wake him up, and say to him, 'Teacher, art thou not caring that we perish?'
Mark 8:35 for whoever may will to save his life shall lose it; and whoever may lose his life for my sake and for the good news' sake, he shall save it;
Mark 9:22 and many times also it cast him into fire, and into water, that it might destroy him; but if thou art able to do anything, help us, having compassion on us.'
Mark 9:41 for whoever may give you to drink a cup of water in my name, because ye are Christ's, verily I say to you, he may not lose his reward;
Mark 11:8 And the scribes and the chief priests heard, and they were seeking how they shall destroy him, for they were afraid of him, because all the multitude was astonished at his teaching;
Mark 12:9 'What therefore shall the lord of the vineyard do? he will come and destroy the husbandmen, and will give the vineyard to others.
Luke 4:34 saying, 'Away, what--to us and to thee, Jesus, O Nazarene? thou didst come to destroy us; I have known thee who thou art--the Holy One of God.'
Luke 5:37 'And no one doth put new wine into old skins, and if otherwise, the new wine will burst the skins, and itself will be poured out, and the skins will be destroyed;
Luke 6:9 Then said Jesus unto them, `I will question you something: Is it lawful on the sabbaths to do good, or to do evil? life to save or to kill?'
Luke 8:24 And having come near, they awoke him, saying, `Master, master, we perish;' and he, having arisen, rebuked the wind and the raging of the water, and they ceased, and there came a calm,
Luke 9:24-25 for whoever may will to save his life, shall lose it, and whoever may lose his life for my sake, he shall save it; 25 for what is a man profited, having gained the whole world, and having lost or having forfeited himself?
Luke 11:51 from the blood of Abel unto the blood of Zacharias, who perished between the altar and the house; yes, I say to you, It shall be required from this generation.
Luke 13:3; 5; 33 No--I say to you, but, if ye may not reform, all ye even so shall perish.; No--I say to you, but, if ye may not reform, all ye in like manner shall perish.'; but it behoveth me to-day, and to-morrow, and the day following, to go on, because it is not possible for a prophet to perish out of Jerusalem.
Luke 15:4; 6; 8-9; 17; 24; 32 'What man of you having a hundred sheep, and having lost one out of them, doth not leave behind the ninety-nine in the wilderness, and go on after the lost one, till he may find it?; and having come to the house, he doth call together the friends and the neighbours, saying to them, Rejoice with me, because I found my sheep--the lost one.; 'Or what woman having ten drachms, if she may lose one drachm, doth not light a lamp, and sweep the house, and seek carefully till that she may find? 9 and having found, she doth call together the female friends and the neighbours, saying, Rejoice with me, for I found the drachm that I lost.; And having come to himself, he said, How many hirelings of my father have a superabundance of bread, and I here with hunger am perishing!; because this my son was dead, and did live again, and he was lost, and was found; and they began to be merry.; but to be merry, and to be glad, it was needful, because this thy brother was dead, and did live again, he was lost, and was found.'
Luke 17:27; 29; 33 they were eating, they were drinking, they were marrying, they were given in marriage, till the day that Noah entered into the ark, and the deluge came, and destroyed all; and on the day Lot went forth from Sodom, He rained fire and brimstone from heaven, and destroyed all.; Whoever may seek to save his life, shall lose it; and whoever may lose it, shall preserve it.
Luke 19:10; 47 for the Son of Man came to seek and to save the lost.'; And he was teaching daily in the temple, but the chief priests and the scribes were seeking to destroy him--also the chiefs of the people--
Luke 20:16 He will come, and destroy these husbandmen, and will give the vineyard to others.' And having heard, they said, 'Let it not be!'
Luke 21:18 and a hair out of your head shall not perish;
John 3:16 for God did so love the world, that His Son--the only begotten--He gave, that every one who is believing in him may not perish, but may have life age-during.
John 6:12; 27 And when they were filled, he saith to his disciples, `Gather together the broken pieces that are over, that nothing may be lost;'; work not for the food that is perishing, but for the food that is remaining to life age-during, which the Son of Man will give to you, for him did the Father seal-- even God.'
John 10:10; 'The thief doth not come, except that he may steal, and kill, and destroy; I came that they may have life, and may have it abundantly.
John 10:28 and life age-during I give to them, and they shall not perish--to the age, and no one shall pluck them out of my hand;
John 11:50 nor reason that it is good for us that one man may die for the people, and not the whole nation perish.'
John 12:25 he who is loving his life shall lose it, and he who is hating his life in this world--to life age-during shall keep it;
John 17:12 when I was with them in the world, I was keeping them in Thy name; those whom Thou hast given to me I did guard, and none of them was destroyed, except the son of the destruction, that the Writing may be fulfilled.
John 18:9; 14 that the word might be fulfilled that he said--`Those whom Thou hast given to me, I did not lose of them even one.'; and Caiaphas was he who gave counsel to the Jews, that it is good for one man to perish for the people.
Acts 5:37 After this one rose up, Judas the Galilean, in the days of the enrolment, and drew away much people after him, and that one perished, and all, as many as were obeying him, were scattered;
Romans 2:12 for as many as without law did sin, without law also shall perish, and as many as did sin in law, through law shall be judged,
Romans 14:15 and if through victuals thy brother is grieved, no more dost thou walk according to love; do not with thy victuals destroy that one for whom Christ died.
1 Corinthians 1:18-19 for the word of the cross to those indeed perishing is foolishness, and to us--those being saved--it is the power of God, 19 for it hath been written, 'I will destroy the wisdom of the wise, and the intelligence of the intelligent I will bring to nought;'
1 Corinthians 8:11 and the brother who is infirm shall perish by thy knowledge, because of whom Christ died?
1 Corinthians 10:9-10 neither may we tempt the Christ, as also certain of them did tempt, and by the serpents did perish; 10 neither murmur ye, as also some of them did murmur, and did perish by the destroyer.
1 Corinthians 15:18 then, also, those having fallen asleep in Christ did perish;
2 Corinthians 2:15 because of Christ a sweet fragrance we are to God, in those being saved, and in those being lost;
2 Corinthians 4:3; 9 and if also our good news is vailed, in those perishing it is vailed,; persecuted, but not forsaken; cast down, but not destroyed;
2 Thessalonians 2:10 and in all deceitfulness of the unrighteousness in those perishing, because the love of the truth they did not receive for their being saved,
Hebrews 1:11 these shall perish, and Thou dost remain, and all, as a garment, shall become old,
James 1:11 for the sun did rise with the burning heat, and did wither the grass, and the flower of it fell, and the grace of its appearance did perish, so also the rich in his way shall fade away!
James 4:12 one is the lawgiver, who is able to save and to destroy; thou--who art thou that dost judge the other?
1 Peter 1:7 that the proof of your faith--much more precious than of gold that is perishing, and through fire being approved--may be found to praise, and honour, and glory, in the revelation of Jesus Christ,
2 Peter 3:6; 9 through which the then world, by water having been deluged, was destroyed; the Lord is not slow in regard to the promise, as certain count slowness, but is long-suffering to us, not counselling any to be lost but all to pass on to reformation,
2 John 8 See to yourselves that ye may not lose the things that we wrought, but a full reward may receive;
Jude 5; 11 and to remind you I intend, you knowing once this, that the Lord, a people out of the land of Egypt having saved, again those who did not believe did destroy; woe to them! because in the way of Cain they did go on, and to the deceit of Balaam for reward they did rush, and in the gainsaying of Korah they did perish.
I'll make a few basic categorizations(that are not mutually exclusive) of ἀπόλλυμι:
(1) The occurrences where ἀπόλλυμι incontrovertibly(indisputably) refers to the end of life(death), whether transitively(e.g. to kill) or intransitively(e.g. to die), are Matthew 2:13; 8:25; 10:39; 12:14; 16:25; 21:41; 22:7; 26:52; 27:20; Mark 3:6; 4:38; 8:35; 9:22; 11:8; 12:9; Luke 6:9; 8:24; 9:24-25; 11:51; 13:3; 5; 33; 15:17; 17:27; 29; 33; 19:47; 20:16; John 11:50; 12:25; 18:14; Acts 5:37; 1 Corinthians 10:9-10; 15:18; 2 Peter 3:6; Jude 5; 11.
(2) The occurrences where ἀπόλλυμι refers to something(always inanimate objects) being totally ruined or rendered useless/unusable are Matthew 9:17; Mark 2:22; Luke 5:37; John 6:27; 1 Corinthians 1:19; James 1:11; 1 Peter 1:7.
(3) The occurrences where ἀπόλλυμι refers either to the act of losing or to the state of being lost are Matthew 5:29-30, 10:6; 39; 42; 15:24; 16:25; Mark 4:38; 8:35; 9:41; Luke 9:24-25; 15:4; 6; 8-9; 24; 32; 17:33; 19:10; 21:18; John 6:12; 12:25; 17:12; 18:9; 2 Corinthians 2:15; 2 Peter 3:9; 2 John 8.
(4) The occurrences where the precise meaning of ἀπόλλυμι is relatively unclear are Matthew 10:28; 15:24; 18:14; Mark 1:24; Luke 4:34; 19:10; John 3:16; 10:10; 28; 17:12; 18:9; Romans 2:12; 14:15; 1 Corinthians 1:18; 8:11; 2 Corinthians 2:15; 4:3; 9; 2 Thessalonians 2:10; James 4:12; 2 Peter 3:9.
Ok, so, what does ἀπόλλυμι refer to in John 3:16? The only conceivable interpretation is that it denotes the end of life, i.e. death(or for some who easily misconstrue, the "separation between body and spirit"). First, we'll consider some competing interpretations.
One competing interpretation is that ἀπόλλυμι -- when used to refer to what happens to the unrighteous at condemnation -- means "ruining or rendering useless". Those who purport this interpretation point to the verses listed in category 2 as proof that ἀπόλλυμι could be saying that the wicked are rendered useless/ruined in such passages as Matthew 10:28, John 3:16, James 4:12, etc. There is a major issue with this interpretation, however. In each of the verses in category 2, ἀπόλλυμι is used with reference to inanimate, lifeless objects(e.g. wineskin, food, wisdom, beauty/grace, gold). Unbelievers at the final eschatological judgment, however, will not be inanimate, lifeless objects, but will be living people after having been resurrected(see Daniel 12:2, John 5:28-29, Acts 24:15). There is no evidence anywhere that ἀπόλλυμι -- when applied to a living, animate being -- can refer to "ruining or rendering useless". Thus, there is no basis for saying that John 3:16 is using ἀπόλλυμι to say that those who do not believe in the Son(i.e. the unrighteous) will be "rendered useless/ruined" at the final judgment.
Another interpretation says that ἀπόλλυμι is used in John 3:16 to refer to being separated/shut out from the presence of God. This fares even worse than interpretation one, as nowhere in the entire New Testament is ἀπόλλυμι incontrovertibly used to denote being separated from God's presence, whether of an inanimate object or one with life! Some point to verses such as Romans 14:15, 1 Corinthians 8:11, and James 4:12 to support their case. But I fail to see how doing so supports this interpretation. Romans 14:15 and 1 Corinthians 8:11 are pretty ambiguous, and it is impossible to prove that ἀπόλλυμι refers to being separated from God's presence.
Romans 14:15 and if through victuals thy brother is grieved, no more dost thou walk according to love; do not with thy victuals destroy[ἀπόλλυμι] that one for whom Christ died.
1 Corinthians 8:11 and the brother who is infirm shall perish[ἀπόλλυμι] by thy knowledge, because of whom Christ died?
I suppose the argument some give goes like this; "Paul is saying that we can 'destroy' our brother by causing them to lose faith in Christ(the one who died for them) through our acts, which in turn causes them to lose their salvation, and hence be condemned; such condemnation is a separation from the presence of God[sometimes they erroneously quote 2 Thessalonians 1:9 to support this conclusion{honestly, just read any literal translation of 2 Thessalonians 1:9 and see how much it doesn't support your theology}]." Of course, this argument commits the logical fallacy of begging the question. "ἀπόλλυμι denotes losing salvation and being condemned and separated from God's presence because condemnation is separation from God's presence" clearly employs circular reasoning. The condemnation could also be eternal death, in which case ἀπόλλυμι(if referring to one losing their salvation) could denote eternal death. Of course, such an argument would also be fallacious, which is why I am not making it.
But Romans 14:15 and 1 Corinthians 8:11 could also mean something other than causing our brother to lose salvation through our acts. Paul could simply be saying that we may greatly discourage our brothers or cause them to stumble(this too, however, can lead to one losing their salvation). Some people do interpret these passages this way(I don't. I interpret it as talking about causing our brothers to lose their salvation). The meaning of ἀπόλλυμι in either of these verses is any BUT clear-cut, and cannot be used to support the notion that ἀπόλλυμι can denote being separated from the presence of God(any argument that attempts to do so will employ circular reasoning). And then there's James 4:12. The situation here is essentially the same.
James 4:12 one is the lawgiver, who is able to save and to destroy[ἀπόλλυμι]; thou--who art thou that dost judge the other?
"Destroy" is contrasted with "save", which unequivocally indicates that ἀπόλλυμι here is referencing final judgment(i.e. condemnation), as it is in Matthew 10:28. But this does NOT support the notion that ἀπόλλυμι can denote being separated from the presence of God. Why? Because the type of destruction(condemnation) being talked about here is not clear-cut and unequivocal! There's no way to prove that ἀπόλλυμι is used to denote the "separation between man and the presence of God". I listed each and every one of the occurrences of ἀπόλλυμι in the New Testament. Can anyone verify that ἀπόλλυμι refers to "being separated from God's presence" in ANY of the passages in which it is used? If not, there is no basis for saying that in John 3:16 ἀπόλλυμι refers to being separated from the presence of God. There is, however, an extensive basis for saying that ἀπόλλυμι denotes death(the end of life) in John 3:16, considering how it is indisputably used in such a manner countless times throughout the New Testament! Thus, the interpretation of John 3:16 that says that those who do not believe in the Son will die(perish) is, by far, the most credible. But there are more reasons why this is so.
Let us now discuss the term "eternal life". The term "eternal life" in John 3:16 in Greek is ζωὴν αἰώνιον, which transliterated is zōēn aiōnion. I see that people have many of their own definitions of "eternal life". In one of the answers already presented(namely, @HoldToTheRod's), "eternal life" has three definitions; "knowing God", "life that is endless in duration", and "life that is godlike in quality"! But there isn't any Biblical basis for "eternal life" being all three of these things. But what about John 17:3? Jesus defines "eternal life" there! Does He, though?
John 17:3 And this is life eternal, that they should know thee the only true God, and him whom thou didst send, even Jesus Christ. (ASV)
I just want to point out that Jesus does not say, "and this is the definition of life eternal, that they should know thee the only true God..." But so what? He uses "is"(present tense third-person singular of "be") to denote that He is identifying/equating "eternal life" with "that they should know thee the only true God", i.e. that "eternal life" and "that they should know thee the only true God" are the same(identical). Perhaps, but such an interpretation is not necessary whatsoever. "Be" is used in many different ways that don't identify one thing with another; this is true today as it was at the time of Jesus. In fact, Jesus frequently used "be" in a way that didn't identify one thing with another.
John 6:63 It is the spirit that giveth life; the flesh profiteth nothing: the words that I have spoken unto you are spirit, and are life. (Jesus says that His words that He has spoken are "spirit" and "life". Does this mean that "spirit" and "life" are defined as "the words that Jesus speaks"? Or is Jesus employing figurative language here? What if Jesus is instead saying that His words are the source of spirit and life, i.e. that listening to what Jesus says will cause us to have spirit and life?)
John 11:25 Jesus said unto her, I am the resurrection, and the life: he that believeth on me, though he die, yet shall he live; (Is Jesus defining Himself as "the resurrection and the life"? I mean, He says that He IS the resurrection and the life, does He not? Or is He once again being figurative? Does He instead mean that He is that which leads to the resurrection and to life, i.e. that He is the means by which we can be resurrected and have life?)
John 12:50 And I know that his commandment is life eternal: the things therefore which I speak, even as the Father hath said unto me, so I speak. (Oof, looks like we're gonna need to add another definition of "eternal life" to our list. :/ Or is Jesus instead saying that the Father's commandment leads to eternal life, that is to say, Jesus' following of the Father's commandment of what to say and speak[see v.49] leads to eternal life? This would corroborate John 6:63, where Jesus says that His words[which we know from John 12:49-50 to be what the Father commanded Him to say] "are spirit and are life".)
John 14:6 Jesus saith unto him, I am the way, and the truth, and the life: no one cometh unto the Father, but by me. (Here Jesus says that He is "the way, the truth, and the life". Is "Jesus" defined as "the way, the truth, and the life"? Or is Jesus instead saying that He is the means by which we are saved, learn the truth, and gain life, i.e. that He is the way to salvation and the source of truth and life?)
For some more examples where "be" is not used to identify/equate one thing with another see John 10:7; 9, 1 John 4:8; 16. So, if in John 17:3 Jesus is NOT identifying/equating eternal life with "knowing the only true God", what is He doing? I propose two possible interpretations. The first is that Jesus is saying that getting to know God can cause us to have eternal life, i.e. that having a relationship with God is what leads to having eternal life. The second is that Jesus is saying that having a relationship with God is the purpose or objective of eternal life, i.e. that the whole point of living for eternity IS to get to know God; to witness the things He does, to listen to the things He speaks, to learn about His character and His attributes(and to love, worship, and adore him thereafter), cf. Matthew 4:4. I normally go with the second interpretation. So, John 17:3 could mean either...
John 17:3 And this is [the purpose of] life eternal, that they should know thee the only true God, and him whom thou didst send, even Jesus Christ.
Or...
John 17:3 And this is [what leads to] life eternal, that they should know thee the only true God, and him whom thou didst send, even Jesus Christ.
There is no reason to think that Jesus means this...
John 17:3 And this is [the definition of] life eternal, that they should know thee the only true God, and him whom thou didst send, even Jesus Christ.
In fact, this would be a considerably less reasonable interpretation. If I say that "Chinese food" is defined, not as "food that originated in China", but as something other than that, e.g. "a wet towel", you'd say I'm a liar. Is Jesus really saying that "eternal life" is not defined as "life that lasts for eternity" but something other than that, i.e. "knowing God"? Or is He speaking figuratively as He does numerous other times in situations analogous to John 17:3?
And what about the notion that "eternal life" is both "life that is endless in duration" and "life that is godlike in quality"? Well, this is undoubtedly far more plausible than the interpretation that "eternal life" is "knowing God"(at least here "life" is part of the equation). Although, I'm not exactly sure how this doesn't disprove traditional eternal conscious separation. ἀπόλλυμι("perish") is presented in contradistinction with(as the antithesis of) ζωὴν αἰώνιον("eternal life"). This would, at the very least, imply that "to perish" means to NOT have "life that is endless in duration" and to NOT have "life that is godlike in quality", would it not? After all, if "eternal life" means having both of these things, then "perish", which is presented in stark contrast with "eternal life", would logically mean having neither of these things, would it not? So, those who do not believe in the Son and "perish"(ἀπόλλυμι) will have neither "life that is endless in duration" nor "life that is godlike in quality", which means their life must end(if it didn't, it would be "endless in duration")... Meaning they die(their "body and spirit separate"). This is more or less annihilationism, you know. It certainly isn't traditional ECT/ECS. Tell me if I'm missing something.
Ok, so what does ζωὴν αἰώνιον mean? Let's examine the words found in the term "eternal life". The word for "eternal" is αἰώνιος(Strong's G166), pronounced aiónios. The word for "life" is ζωή(Strong's G2222), pronounced zōē. The Greek word "αἰώνιος" isn't too complicated. Both Strong's Exhaustive Concordance and Thayer's Greek Lexicon state that αἰώνιος can be applied to something without an end, i.e. something that everlasting, perpetual, continuous, unending, etc. So, the most unambiguous interpretation of the term "ζωὴν αἰώνιον" is "ζωή that lasts forever(without end)". Ok, what does ζωή mean? Strong's Concordance on ζωή is rather straightforward(Thayer's has a lot more to say though). It says that ζωή means life or lifetime. The English word "life" has multiple meanings to it, but there are two primary meanings that correlate to how ζωή is used in the NT:
(1) "the condition or quality that distinguishes a vital, functional, animate being from an inanimate/inert object[e.g. a dead body]", as in the sentences "the doctor saw no signs of life" and "all living creatures have life in them".
(2) "the period of embodied existence of an individual", as in the sentences "my kids are the joy of my life" and "I've experienced a lot in my life".
These two definitions of "life" are very closely linked and at times interchangeable. For example, "death" is defined as the end of life. But which meaning of "life" is death the end of? Is it the end of someone's period of embodied existence or the end of the quality that distinguishes between functional beings and inanimate objects? Yes! Death is the end of both of these.
Anyway, ζωή can indisputably refer to either of these definitions of "life"(see Luke 12:15, Luke 16:25, Acts 8:33, Acts 17:25, Philippians 1:20, 1 Timothy 4:18, Hebrew 7:3, James 4:14, 1 Peter 3:10), as confirmed by Thayer's. I believe that the second definition of "life" is in view in the term "eternal life", making "eternal life" a period of embodied existence that lasts for eternity. This is the most reasonable, considering how life(ζωή) and resurrection are closely linked in scripture(e.g. John 5:21; 28-29; 6:40; 11:25), and considering how we are resurrected in immortal, imperishable bodies, meaning we will have endless embodied existence(see 1 Corinthians 15:35-55 cf. Romans 2:7, 2 Timothy 1:10). Thus, the most straightforward interpretation of the term "ζωὴν αἰώνιον" is an eternal period of embodied(bodily) existence.
We will discuss what "perish" means in the context of John 3:16 in the next answer. Hope this helps! :)
Whatever one makes of the verb ἀπόλλυμι, John 3:16 paints it as the opposite of eternal life.
Both BDB and Thayer both list several meanings for ἀπόλλυμι, but both agree that in John 3:16 it means to perish, destroy utterly, be ruined, etc. It is similar that same meaning in other places such as:
... and so forth. ἀπόλλυμι refers to eternal death when in contradistinction with eternal life. The Bible does not say how long this takes (assuming it occurs in gehenna). See Matt 10:28.
This is part two of our discussion on John 3:16 (read part 1 if you haven't already ^_^). We had concluded that the term "eternal life"(ζωὴν αἰώνιον) most likely refers to the eternal period of embodied (bodily) existence. This is most plausible, considering how Jesus promises to resurrect us TO life(ζωή) in immortal, imperishable bodies (see John 5:21; 28-29; 6:40; 11:25; 1 Corinthians 15:35-55, cf. Romans 2:7, Romans 8:11, 2 Timothy 1:10, Revelation 20:6), which means that our resurrected bodies will last forever, meaning we will have endless embodied existence. We also concluded that there is no basis for saying that ἀπόλλυμι refers to unbelievers "being rendered useless/ruined" in John 3:16, as such an application only ever occurs in conjunction with inanimate, lifeless objects (of which those a part of the resurrection of the unrighteous will decidedly not be).
We also concluded that there is no basis for saying that John 3:16 uses ἀπόλλυμι to say that unbelievers will be "separated from the presence of God", as it is impossible to prove that ἀπόλλυμι is ever used to refer to "being separated from God's presence". If I can't prove the validity of a certain denotation of a word, then how can I plug in said denotation where the word is used? I can say that the word "bark" can refer to "jumping on a bed". But if I can't prove it, do I have the right to plug in this meaning of "bark" into a sentence that contains the word, e.g. "the dog will bark[jump on a bed] loudly at you"? Of course not (even if I could prove the validity of that denotation of "bark", the context would clearly forbid me from plugging that meaning of "bark" into the text. Many factors have to be taken into account when determining the meaning of a word [when performing Biblical exegesis, one cannot simply assume that all shades of meaning of a word are available to the interpreter in every context])! Until you can prove that ἀπόλλυμι can be used to denote "being separated from the presence of God", there are absolutely no grounds for saying that John 3:16 is using ἀπόλλυμι in such a manner. Finally, we concluded that ἀπόλλυμι, in John 3:16, is most likely referring to "death", as it unequivocally does countless other times in the New Testament. We will now discuss what "perish" means in the context of John 3:16, and hence further substantiate this conclusion.
John 3:14-16 And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up; 15 that whosoever believeth may in him have eternal life. 16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth on him should not perish, but have eternal life. (ASV)
John starts off with, "and as Moses lifted up the serpent in the wilderness". John is making an allusion to Numbers 21:4-9. Let's read the passage.
Numbers 21:4-9 From Mount Hor they set out by the way to the Red Sea, to go around the land of Edom. And the people became impatient on the way. 5 And the people spoke against God and against Moses, “Why have you brought us up out of Egypt to die in the wilderness? For there is no food and no water, and we loathe this worthless food.” 6 Then the Lord sent fiery serpents among the people, and they bit the people, so that many people of Israel died. 7 And the people came to Moses and said, “We have sinned, for we have spoken against the Lord and against you. Pray to the Lord, that he take away the serpents from us.” So Moses prayed for the people. 8 And the Lord said to Moses, “Make a fiery serpent and set it on a pole, and everyone who is bitten, when he sees it, shall live.” 9 So Moses made a bronze serpent and set it on a pole. And if a serpent bit anyone, he would look at the bronze serpent and live. (ESV)
The Israelites, while on a journey around the land of Edom, became impatient and started to speak against God and Moses. As a result, Yahweh sent fiery serpents to bite and kill the Israelites as punishment. Many Israelites died (to be sure, their "spirit separated from their body"). Naturally, they repented, and so Moses prayed to God for the people. God responded by telling Moses to make a fiery serpent and set it up on a pole so that everyone who is bitten by the fiery serpents could gaze upon it and live (to be sure, their "spirit remained in union with their body"). When Moses did what Yahweh asked, made the serpent out of bronze, and set it on a pole, anyone who was bitten by the serpents God had previously sent forth could look upon the bronze serpent and be saved from death, that is, they could keep their life.
John says "AS Moses lifted up in the serpent... so must the Son of man be lifted up". John is showing that the account in Numbers 21:4-9 was a type of what happened with Jesus, which is the antitype, that is to say, it prefigured or foreshadowed what would happen with Jesus. In what way was the account a type? John goes on to tell us; "that whosoever believeth may in him have eternal life". In the same way that the elevated bronze serpent saved the Israelites' lives from death, so the Son of man saves our life from death. Except the "life" and "death" in question are eternal life and death, hence why Jesus' situation is the antitype to the account in Numbers 21:4-9 (that the antitype is greater in significance than the type is sort of the whole point). And to make sure we fully get the point and aren't missing anything, John continues... "For God so loved the world, that he gave his only begotten Son, that whosoever believeth on him should not perish, but have eternal life." Whosoever gazed upon the bronze serpent did not perish but lived; whosoever believes upon God's only-begotten Son will not perish but live forever! Believing in Jesus does not save us from "separation from the presence of God", just as looking upon the bronze serpent did not save the Israelites from "separation from the presence of God". As the bronze serpent saved the Israelites from death ("separation between body and spirit"), so does God's only-begotten Son (otherwise the type-antitype is meaningless). In the same way that everyone who did not gaze upon the bronze serpent did not survive the snakebite and died, everyone who does not believe in Jesus will not survive God's coming judgment and will die(perish). Hence, the type-antitype situation. As we can see, John is clearly talking about literal death here (to be sure, "separation between body and spirit"). Can ἀπόλλυμι be used to refer to death? We'd already firmly established that, not only is this the case, but it is the only plausible interpretation! This further supports this conclusion.
Finally, we will discuss the stark contrast between ἀπόλλυμι("perish") and ζωὴν αἰώνιον("eternal life") in John 3:16. They are presented as antithetical fates; if you believe in God's Son, you will necessarily have ζωὴν αἰώνιον, which necessarily entails that you will NOT ἀπόλλυμι. This, in addition to the aforementioned, makes it abundantly clear that "ἀπόλλυμι" refers to literal perishing/dying (and doing so with eternal consequences). Having "eternal life" and "perishing" are mutually exclusive(and in all likelihood jointly exhaustive) destinies. If ἀπόλλυμι("perish") refers to dying such that you are dead forever, then certainly you cannot have eternal life (eternal embodied existence); you can't be dead forever and alive forever simultaneously! Those who do not believe in the Son will die(ἀπόλλυμι) and stay dead for eternity and thus will not have eternal life(ζωὴν αἰώνιον); those who do believe in the Son will have eternal life(ζωὴν αἰώνιον) and thus will not die(ἀπόλλυμι) and stay dead for eternity1. In conclusion, ἀπόλλυμι, in John 3:16, means to die/to perish, i.e. to have your life cease to exist(or, to have your "spirit separated from your body").
The fact that John is speaking about eternal life means that he is (probably) talking about the final eschatological judgment here (see Matthew 25:31-46), which is subsequent to the millennium, according to Revelation 20:7-15. The life that those who believe in the Son receive is everlasting (perpetual, unending); the punishment2 that those who do not believe in the Son receive is likewise everlasting (perpetual, unending), and said punishment is revealed to us by John to be death (i.e. those who do not believe in the Son will "perish"[ἀπόλλυμι]).
The Bible doesn't tell us precisely how long, though we know it cannot take forever. "Perish" is a telic verb, meaning it tends to a definite end. If the process of perishing lasts for eternity, then you never actually perish, do you? If you did perish, then the process would end; but something that is eternal, by definition, never ends! Let me reiterate; if you continue to "perish" for eternity, you never actually perish, because if you did, the process would end, and something that goes on for eternity, by definition, never ends. So, we know with certainty that those who "perish" do not do so for eternity; they necessarily "perish" in a finite amount of time.
1 I think a passage that largely substantiates the notion that "eternal life" refers to eternal embodied existence and "perish" refers to eternal death is 1 Corinthians 15:16-19. If Christ was not raised from the dead, our faith is utterly in vain(futile), and those who have died in Christ have perished(ἀπόλλυμι), i.e. they will be dead for eternity (they will never be resurrected to embodied existence). Do these ones have eternal life? No, if they did, they would not have "ἀπόλλυμι" ("perishing"[ἀπόλλυμι] is presented as diametrically opposed to "eternal life"[ζωὴν αἰώνιον] in John 3:16 and John 10:28[both verses speak about believers receiving "eternal life" and as a consequence not "perishing"])! In verse 19, Paul says that if we only have hope in Christ in this life (i.e. in this period of embodied existence), we are to be pitied the most (our hope is in endless bodily existence that takes place in the next life, not this one. This is only possible due to Jesus first being resurrected to eternal embodied existence. If He wasn't, then our hope is limited to this period of embodied existence only; we have no hope for another life. Surely then we are to be pitied the most). The main reason why believing in Jesus leads to eternal life (John 3:16) is because of the fact that He was raised from the dead to eternal embodied existence, that is, He himself was resurrected to "eternal life" (it is due to this fact that He is now able to give us life[see v.45]. We receive eternal life because Jesus gives it to us, and Jesus gives it to us because He was resurrected with the capacity to give eternal life, He Himself receiving it[cf. Revelation 1:18]). Christ was the firstfruits of those to follow Him(see v.20 and v.23), that is to say, what He was given (i.e. eternal embodied existence by means of a resurrection), we are likewise given, but only because He was first given it. If He was never resurrected to eternal embodied existence (eternal life), we would never be resurrected to eternal embodied existence (eternal life), that is, we would be in death for eternity, and precisely what word does Paul use to describe this dreadful scenario? ἀπόλλυμι, the very word under consideration in John 3:16, where it is contrasted with "eternal life" (which we would not receive had Christ not been raised from the dead)! If a New Testament author wanted to refer to "eternal death", ἀπόλλυμι is precisely the word that they would use! One cannot say the same about eternal conscious separation.
2 Many people believe that Matthew 25:46 proves eternal conscious torment, but it doesn't. First of all, Jesus says that the wicked will go into "eternal punishment", not "eternal punishing", which would mean that God continually punishes the wicked for eternity, and would indicate eternal conscious torment. Second of all, punishment is defined as "a penalty inflicted on an offender through judicial procedure" (the word for "punishment" in Greek, κόλασις[kólasis], is the same, and refers to a "penal infliction", according to Strong's G2851). Notice that there isn't anything about torment. Certainly, torment can be a punishment inflicted upon someone. But it is not the only punishment that can be inflicted upon someone. Death is also a punishment (in today's societies, it is capital punishment). So, "eternal punishment" can refer to "eternal death" just as it can refer to "eternal torment". In fact, the context highly suggests the former. "Eternal life" and "eternal punishment" are presented, by Jesus, as irreconcilable futures on opposite ends of the spectrum. On the one hand, you have the righteous, blessed by their Father, who go into eternal life and, consequently, not into eternal punishment. On the other hand, you have the workers of lawlessness, the cursed who depart from Christ (cf. Matthew 7:23) into eternal punishment and, consequently, not into eternal life. Hence, whatever their punishment is, we know that it precludes eternal life, otherwise, there'd be no distinction between them and the righteous in that regard (and Jesus makes an unequivocal distinction between the two in that regard). Necessarily, then, their punishment, which lasts for eternity according to Jesus, must, at the bare minimum, include death somewhere down the line. If those who go into the punishment don't eventually die, then they would live forever, and then they would have received eternal life. This makes anything that doesn't include death ruled out as a possibility for what the "eternal punishment" spoken of by Jesus might be. Indeed, contrary to popular opinion, Matthew 25:46 is actually better support for conditionalism than traditionalism.
Hope this helps. :)
