What's in a name
There is a play on words here (in Hebrew) that sheds light on this verse. The play on words does not work in Greek or English, which has caused many to scratch their heads at this verse over the years.
Jesus' name in Hebrew is Yeshua (ישוע--more than one vocalization has been suggested), which derives from "to rescue" or "to deliver". So the angel is telling Mary that her Son will be named a rescuer/deliverer because...that's what He is going to do. This is the same root as יְשׁוּעָה, meaning salvation (see Strong's 3444).
Jesus' name, and the angelic pronouncement of the purpose for the name, then point to the Old Testament promises of salvation, such as:
Behold, God is my salvation; I will trust, and not be afraid: for the
Lord Jehovah is my strength and my song; he also is become my
salvation. (Isaiah 12:2, note the same root יְשׁוּעָה again )
This background is helpful because it points to the Old Testament context of what the Savior is supposed to do.
Which Savior? The Savior:
I, even I, am the Lord; and beside me there is no saviour. (Isaiah 43:11)
Penalty of Sin
That the Savior was to bear the penalty of sin is powerfully stated by Isaiah:
But he was wounded for our transgressions, he was bruised for our
iniquities: the chastisement of our peace was upon him; and with his
stripes we are healed. (Isaiah 53:5)
There was a price to be paid, and Jesus paid it. Note that not only did He pay for the wrongs we have done, He paid for the wrongs other people have done. So when someone wrongs me and I feel angry, I think they should be punished, I think there is a price to be paid, I need to remember: that price was already paid.
We do not in vengeance extract a penalty for sin from other people because the Savior has already offered payment in full.
Bondage of sin
That the Messiah was to deliver His people from bondage is all over the Old Testament symbolism. Perhaps most notably through the Passover, Israel's deliverance from physical bondage, which was a type/symbol for the deliverance from bondage to be given by the Messiah.
John is careful to point out that Jesus is the Passover lamb, including:
- "Behold the Lamb of God, which taketh away the sin of the world." (John 1:29)
- Showing in his passion narrative that Jesus died on the afternoon of 14 Nisan, as the Passover lambs were being slaughtered.
Jesus is the ultimate deliverer, prophesied directly and through symbols in the Old Testament. He is the Passover lamb who delivers from bondage.
A Bondage Application: Addiction
What does it mean to deliver from bondage? John already told us it involves taking away the sin of the world. Let's look at one other specific application, which I believe has very direct bearing on the OP's question about the bondage of sin and what it sometimes looks like.
Addiction is a powerful force that destroys many lives.
6 Is not this the fast that I have chosen? to loose the bands of
wickedness, to undo the heavy burdens, and to let the
oppressed go free, and that ye break every yoke?
8 Then shall thy light break forth as the morning, and thine health
shall spring forth speedily: and thy righteousness shall go before
thee; the glory of the Lord shall be thy rearward.
9 Then shalt thou call, and the Lord shall answer; thou shalt cry, and
he shall say, Here I am. If thou take away from the midst of thee the
yoke, the putting forth of the finger, and speaking vanity; (Isaiah
God offers redemption from even the most tightly bound burdens and the heaviest yokes. How does this happen? By coming unto Christ (which fasting is designed to help with):
28 Come unto me, all ye that labour and are heavy laden, and I will
give you rest.
29 Take my yoke upon you, and learn of me; for I am meek and lowly in
heart: and ye shall find rest unto your souls.
30 For my yoke is easy, and my burden is light.
One of the great bondages of sin is to become trapped in the yoke of addiction. The Savior gives commands to help prevent people from becoming trapped in the first place, and mercifully He also offers the redemptive power to break free when people have fallen in.
My thoughts in greater depth on this bondage--and God's answer to it--can be found in the parable here and its interpretation here.
To make holy
Most definitely Jesus offers freedom from the bondage of sin. When people are freed from addiction they not only have something taken out of their lives, but they are changed (if not they will relapse--true addiction recovery requires a change).
By freeing us from this bondage and purging it from our lives like a refiner's fire, He can make us not only clean (sins remitted), but indeed change our nature--He can make us holy.
That this was the intended symbolism of the Levitical sacrifices and the effect of Jesus' atonement is addressed in Hebrews:
13 For if the blood of bulls and of goats, and the ashes of an heifer
sprinkling the unclean, sanctifieth to the purifying of the flesh:
14 How much more shall the blood of Christ, who through the eternal
Spirit offered himself without spot to God, purge your conscience from
dead works to serve the living God? (Hebrews 9:13-14)
The word sanctify means "to make holy".
(A much longer version of my thoughts on how His grace makes people holy is found here).
Jesus came in fulfilment of the Old Testament prophecies of deliverance from the bondage of sin and the penalty of sin.
If we say that we want God to forgive us of our sins but allow us to continue along exactly as we were before, then we have entirely missed the point. Christ's atoning sacrifice is designed not only to make people clean, but to make them holy.