NOTES for Jer 31:33-34
This passage is the fullest exposition of what the New Covenant is. It is interesting that this exposition is contained in the Old Testament, meaning that God warned people in advance, six centuries earlier, about what He intended to do for our salvation. It is worth pondering the meaning of these words.
"I will be their God, and they shall be My people" is the formula of what God offered people already in the covenant with Moses, what is fulfilled if people fulfill God's law. The problem is that the law is not fulfilled. Human sinfulness, slavery to sin, gets in the way. This is precisely what the New Covenant deals with. So God says: "I will put My law within them and write it on their hearts," that is, God promises to make the law not an external institution for the human person, but an inner need motivated by "knowledge of God," a deep personal connection with Him. But sin separates the human person from God, and therefore God is going to destroy, "remember no more," this barrier. How? "I will forgive their iniquities," by forgiveness of sins. Now remember the Gospel and you will agree that it tells of the fulfillment in Jesus Christ of all these promises of God.