NOTES for Jer 31:33-34
It is interesting that this text is of the Old Testament, but speaks about the New, that is God warned people beforehand, 6 centuries ago, of what He is going to do for our salvation. It is really necessary to think about the meaning of these words.
"[I] will be their God, and they shall be my people.", it is a formulation of what God proposed to people still in the covenant with Moses, what comes true, when people fulfill God's law. The problem is that God's law is not being fulfilled. The human sinfulness, slavery to sin disturbs. And here is what the New Testament is all about. Thus, the Lord says: "I will put my law in their inward parts, and write it in their hearts", - which means God promises to make the law not to be an external establishment for the person, but his internal, motivated by " the knowledge of God", a profound personal contact with Him. But sin indeed, separates man from God, that is why God is going to destroy (" will remember no more") this barrier. How? "I will forgive their iniquity" - the forgiveness of sins. And now remember the Gospel - and you will accept that it tells about the fulfillment of all God's promises in Jesus Christ.