These are the rest of the songs of ascents. Psalm 130 is a prophetic Psalm that shows what Israel is ultimately all about, redemption from sin.
3 If you, Lord, kept a record of sins,
Lord, who could stand?
4 But with you there is forgiveness;
therefore you are feared.
The writer knows somehow in some way the Lord will not keep a record of sins. But then how can he remain just, for sin must be punished. The Covenant of Works is all throughout the OT. There is law, but here we see gospel, as we see in the final two verses:
7 Israel, put your hope in the Lord,
for with the Lord is unfailing love
and with him is full redemption.
8 He himself will redeem Israel
from all their sins.
The payment for sin will come from God himself. In hindsight it is easy to see that this could only be done by Christ, by God himself becoming man, and paying the penalty, taking our guilt upon himself. Thus he himself does the redeeming. For the followers of Jesus, however, this was inconceivable.
There are other Messianic references in these Psalms as well. In 132:
10 For the sake of your servant David,
do not reject your anointed one.
11 The Lord swore an oath to David,
a sure oath he will not revoke:
“One of your own descendants
I will place on your throne.
12 If your sons keep my covenant
and the statutes I teach them,
then their sons will sit
on your throne for ever and ever.”
Ah, but none of the sons can keep God’s covenant, except one. Jesus was that descendant. And as you read on, God says Zion is dwelling place, and here we have a direct prophecy of the incarnation:
14 “This is my resting place for ever and ever;
here I will sit enthroned, for I have desired it.
So one of David’s descendants will sit on his throne, thus he will be a man, and God says he himself will “sit enthroned.” It’s difficult to get much more clear than that. It will the the God-man. And his sons, his children, i.e. us, will rule with him forever. And the final two verse make it even more abundantly clear:
17 “Here I will make a horn grow for David
and set up a lamp for my anointed one.
18 I will clothe his enemies with shame,
but his head will be adorned with a radiant crown.”
Christ, God in flesh, came the first time in mercy to redeem his people, he will come again and be vindicated in his justice. As Paul tells is in Philippians 2, because of his obedience to death on a cross:
9 Therefore God exalted him to the highest place
and gave him the name that is above every name,
10 that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
11 and every tongue acknowledge that Jesus Christ is Lord,
to the glory of God the Father.