In the last part of verse 34 God says, "I will forgive their iniquity, and their sin I will remember no more." As we pointed out in the previous message, this involves redemption (Eph. 1:7). Since God forgives, to know God is to forgive others and to not remember their sin. This is to live out Christ's redemption.
All the matters in Jeremiah 31:33 and 34 are developed in the New Testament. In Hebrews 8 Paul quotes these verses in order to show us that today we have the inner law, the law of life. In the new covenant, which is the better covenant (Heb. 7:22), God has put Himself into us as life, and this life is our inner law. This inner law is our capacity to live God in order to be God's people. Thus, we can live and have our being in the same way God does. He is forgiving and does not remember the sins of His people, and we can be the same.
What is described in Jeremiah 31:33 and 34 is actually the new creation. The ultimate issue of Jeremiah's revelation is the new creation, which will consummate in the New Jerusalem. Therefore, intrinsically speaking, Jeremiah is the same as the New Testament. The intrinsic content of the book of Jeremiah is the base of the New Testament. The New Testament is thus the development of Jeremiah.
The book of Jeremiah, which is full of speaking concerning Israel's sin and God's wrath, chastisement, and punishment, reveals that God wants to be the fountain of living waters for our satisfaction in order to produce His increase for His expression. Even though we have failed, He does not fail. It is of His lovingkindness that we are not consumed, and His compassions do not fail but are new every morning. God's compassions upon us in our failure prepare the way for Christ to come in first to be our righteousness and then our redemption and our life. Righteousness, redemption, and life with its law and capacity—all these are Christ. It is by such a righteousness, redemption, and life that God makes Christ everything to His elect. Christ is the center and the circumference of God's people, and He is also the centrality and universality of God's dealing with all the peoples on earth. This is the intrinsic content of the book of Jeremiah.