I. BIBLE FRAMEWORK FOR TRUE INTERPRETATION
First, John was fully aware of the significance of and interpretation for this verse. Jesus opened his eyes. See:
Lk 24:45 Then he opened their minds to understand the Scriptures..
Also, the Book of John ties the whole Bible together.
Before I go into the specific interpretation of John 19: 34 & 33 let us look at several important verses that have to do with the right approach to true interpretation (read these very carefully):
** "ANCHOR" VERSES FOR PROPER INTERPRETATION **
(ESV) 1 Cor 4:6 I have applied all these things to myself and Apollos for your benefit, brothers, that you may learn by us not to go beyond what is written, that none of you may be puffed up in favor of one against another.
Deut 12:32 “Everything that I command you, you shall be careful to do. You shall not add to it or take from it.
Rev 22:18 I warn everyone who hears the words of the prophecy of this book: if anyone adds to them, God will add to him the plagues described in this book,
19 and if anyone takes away from the words of the book of this prophecy, God will take away his share in the tree of life and in the holy city, which are described in this book.
(My note: I placed this verse here because the same language is used in several other places in the Bible. It means this also applies to the whole Bible -see Is 46:10 below.)
Prov 30:5 Every word of God proves true; he is a shield to those who take refuge in him.
6 Do not add to his words, lest he rebuke you and you be found a liar.
(My note: The above 4 sets of verses are collectively telling us not to add in anything, including our own ideas or assumptions nor omit anything that is Biblical.)
Hos 4:6 My people are destroyed for lack of knowledge; because you have rejected knowledge, I reject you from being a priest to me. And since you have forgotten the law of your God, I also will forget your children.
2 Cor 5:16 From now on, therefore, we regard no one according to the flesh. Even though we once regarded Christ according to the flesh, we regard him thus no longer.
(My note: this means we are no longer to approach the bible with a "human" point of view nor treat it as a literary or academic work or as poetry, etc. as that is not what the Bible is about. The Bible is the textbook of life, what it is & what it is not from God's point of view.)
Jn 3:30 He must increase, but I must decrease.”
(My note: John the Baptist was a human like us, indicating that our "humaness" must decrease, while Jesus must be increased within us, pointing to the verse above this one.)
1 Cor 10:11 Now these things happened to them as an example, but they were written down for our instruction, on whom the end of the ages has come.
2 Pet 1:19 And we have something more sure, the prophetic word, to which you will do well to pay attention as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts,
20 knowing this first of all, that no prophecy of Scripture comes from someone’s own interpretation.
21 For no prophecy was ever produced by the will of man, but men spoke from God as they were carried along by the Holy Spirit.
Jn 5:39 You search the Scriptures because you think that in them you have eternal life; and it is they that bear witness about me,
Jer 31:36 “If this fixed order departs from before me, declares the Lord, then shall the offspring of Israel cease from being a nation before me forever.”
(My note: The fixed order of the universe & the earth & things on earth are the fixed "earthly" things used in the Bible which the Bible uses to describe & explain the fixed "Heavenly" things = God & Jesus do not change and neither does the truth that stands forever unchanged.)
Hos 5:10 The princes of Judah have become like *those who move the landmark; upon them I will pour out my wrath like water.
(My note: There are both physical & Spiritual landmarks in the Bible.)
Lk 16:17 But it is easier for heaven and earth to pass away than for one dot of the Law to become void.
(My note: In other words, everything written in the Bible has a fixed position & we are not allowed to change anything, including its meaning & interpretation.)
Is 46:10 declaring the end from the beginning and from ancient times things not yet done, saying, ‘My counsel shall stand, and I will accomplish all my purpose,
(My note: In other words, the etire Bible is a prophecy, having many parts through out the whole Bible -i.e. At the end God shall once again divide the waters from the waters, this time permanently.)
*Jn 3:12 If I have told you "earthly" things and you do not believe, how can you believe if I tell you "heavenly" things?
(My note: This is probably the most important "anchor" verse in the whole BIble as it is the base on which all true Biblical interpretation rests, using things we can see to show & explain Heavenly things to us that we can't see.)
ANCHOR VERSES: The above verses are what I call "anchor" verses. They set the boundaries, limits and God's fixed order that we must stay within if we intend to find and adhere to true interpretation, as given by God through Jesus not man. While the first answer for this question "almost" goes to the right interpetation, it drops the ball and then adds error.
II. JOHN 19:34 INTERPRETATION
Jn 19:34 But one of the soldiers pierced his side with a spear, and at once there came out blood and water.
The first thing we must do is look at earthly things connected to this verse in order to begin to understand the true interpretation for what its trying to tell us. The first thing that will help us understand this verse is to understand more about "bones" relative to Jesus. We need to look at:
Jn 1:14 And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
We also know the Bible is the word of God. Therefore, Jesus is the Bible (given to us to enlighten us about God, Jesus and Heaven & about the problems & faults that can prevent us from knowing these things -our unrighteousness gets in the way).
** BONES **
See Jn 19:33 But when they came to Jesus and saw that he was already dead, they did not break his legs.
The OT covenant was rigid. It has a set of laws & violation of the law brought serious consequences, some immediate. Since Jesus is the word, the OT is Jesus' skeleton made up of bones, one of which is a rib (blood is made in the bone marrow). The NT is Jesus' flesh. Flesh is soft, pliable =the NT covenant brings in grace and forgiveness. Jesus' leg was not broken because Jesus fulfilled the law. He never broke the law. Bones give form (& strength) to our flesh. While under the NT covenant the OT law is to guide us giving form to our life in Jesus. (The Romans unknowingly fulfilled Scripture as many do today.)
** BLOOD **
In the OT you will find the term "life blood". See:
Lev 17:14 For the life of every creature is its blood: its blood is its life.  Therefore I have said to the people of Israel, You shall not eat the blood of any creature, for the life of every creature is its blood. Whoever eats it shall be cut off.
Blood goes to all living cells, bringing everything they need to keep them alive. Now look at:
Jn 6:63 It is the Spirit who gives life; the flesh is no help at all. The words that I have spoken to you are spirit and life.
Now we apply Jn 3:12 (see "anchor" verses above). Therefore, the more important understanding is that blood has a direct connection to the Holy Spirit & the NT covenant (the OT has more to do with "earthly" things & the NT has more to do with "Heavenly" things relative to earthly things).
** WATER **
Now what about water? Humans need to drink water every day or you will dry out, that is you will dehydrate. Water also gives us nutrients and minerals. However, an important point, water must be "processed" to be useful to our bodies. See:
Rev 10:9 So I went to the angel and told him to give me the little scroll. And he said to me, “Take and eat it; it will make your stomach bitter, but in your mouth it will be sweet as honey.”
Your stomach processes food & water while your mind processes the word of God (the more you study the Bible the more Spiritual water Jesus can "pour" into you):
Ref, =Job 34:3 for the ear tests words as the palate tastes food.
Water is also used to carry impurities out of our bodies (purification -the word is for purification of our minds). We also use water to cleanse our bodies. In other words, the use of the word "water" in the Bible is regarding the fact that the word was given to us to give us Spiritual nourishment, to keep us Spiritually hydrated and is for our Spiritual purification as we pursue knowing and following Jesus. We must also be aware that water can destroy and be used to destroy people, even those whom misuse or use it in wrong ways.
The word is also giving us directions on how to live and build a true "Spiritual" church of God. Equating and applying the term "eternal life" or "Spirit" to water is a wrong application as it sets a limit on what "Eternal Life" encompasses. Eternal life & what that is about is what the whole NT speaks to and the OT points to. Eternal Life (a gift to the saved from God) exists on it own, separate from any processing, which is not the case with regard to the use of water. See:
Jn 1:33 I myself did not know him, but he who sent me to baptize with water said to me, ‘He on whom you see the Spirit descend and remain, this is he who baptizes with the Holy Spirit.’
(My note: Notice that water & the Spirit are being referred to separately here. This is an important distinction. Water [the word] leads us to what is Spiritual. In other words, the word explains to us what is Spiritual and what is not.)
Spiritual water brings us "toward" eternal life but, again water isn't eternal life -indicated here:
Jn 4:14 but whoever drinks of the water that I will give him will never be thirsty again. The water that I will give him will become in him a spring of water welling up to eternal life.”
Gen 1:2 The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters.
(My note: We can drink water but you can't drink eternal life. The Spirit of God is above & moves the water but is not within the water molecules themselves.)
Like we need to drink water every day we need to read the Bible every day. See:
Acts 17:11 Now these Jews were more noble than those in Thessalonica; they received the word with all eagerness, examining the Scriptures daily to see if these things were so.
** THE SECOND ADAM AND EVE **
1 Cor 15:45 Thus it is written, “The first man Adam became a living being”; the last Adam became a life-giving spirit.
(My note: Here we see that there is a relationship between Adam [sinner] in the Garden of Eden and Jesus [perfect], God's life-giving Spirit.)
Now we can apply all these things to verse 34 to see the proper interpretation of its contents:
What is the significance of blood & water "pouring" out of Jesus' side? First, there was the "earthly" imperfect sinner, Adam (the 1st chosen, not necessarily the 1st human). Jesus is the Second "Heavenly" perfect sinless Adam. Like the first Adam Jesus had His side opened. In the case of Adam, God put him into a deep sleep and made "earthly" Eve using a part of Adam, his rib (there are "laws" [God knows & used Laws of Physics] involved in creating things, which would have been followed for the creation of Eve.
Adam, being created as the dominent one (a leader) he would have "poured" himself (both his spirit & his knowledge to become one flesh) into Eve, a kind of vessel (so that she would know him, become a better helper & doing this would also make her better at raising his children). You will notice that in making Eve from Adam it doesn't mention God giving Eve the breath of life as she was made out of "living" Adam.
The same is true regarding Jesus (the Bridegroom). See:
Jn 3:29 [John the Baptist speaking about Jesus] The one who has the bride is the bridegroom. The friend of the bridegroom, who stands and hears him, rejoices greatly at the bridegroom’s voice. Therefore this joy of mine is now complete.
Jesus' death (a deep sleep) was needed to bring forth the new more perfect Eve, that is the birth of the Spiritual church (the Spiritual "mother" of Jesus' church, Spiritual Israel (not the Catholic version), the second Eve, the bride to be). The new Eve is conceived by the "pouring" out of Jesus, the "life" blood (Jesus' Spirit giving life to His church, through Spiritual Physics =the Spiritual rib) and the "pouring" out of water (the word =the Bible) to His bride, the new more perfect Spiritual Israel. See the following verses:
Rev 19:7 Let us rejoice and exult and give him the glory, for the "marriage of the Lamb" has come, and his Bride has made herself ready.
(My note: This is why Jesus never married on earth.)
Jn 1:29 The next day he saw Jesus coming toward him, and said, “Behold, the Lamb of God, who takes away the sin of the world!
Heb 9:24 For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf.
25 Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own,
26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself.
27 And just as it is appointed for man to die once, and after that comes judgment,
28 so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.
(My note: In order for the OT covenant to end it was a requirement that it be fulfilled in full. Jesus was the pefect sacrifice [the Lamb of God], whom fulfilled the OT Law even becoming the absolute perfect sacrifice to once and for all have the ability to take all the sins of the world upon Himself, thus terminating the OT covenant.)
1 Pet 2:5 you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ.
The major issue is that one must be very careful when trying to interpret Scripture. Many have made the mistake of putting forth wrong interpretations (intentionally & unintentionally). Even to this day many are still paying for these mistakes, some fatal for many. I can't stress this enough, be very careful not to go beyond what is written.