In Jeremiah 31, the glorious promise of a New Covenant is made, but not everything was glorious. The promise was made to God's people while they were suffering for their sins in another country and having lost every physical blessing of the covenant. Yet, the Lord of the Covenant gave God's people the promise of an even greater blessing.
In verse 31, the Lord exhorted the people to behold the promise. Of course, they could not see it with their physical eyes. All around them were the signs of God's displeasure. So, what He is exhorting His people to do is to perceive with the eyes of faith. He is calling them to trust in His promise - He calls us to trust in the same promise. That promise is the promise of a New Covenant that He will make with His people. Again, the Lord of the Covenant takes the initiative as the Sovereign and declares that He will do this. Even though the Lord was justly angry with sin, His mercy and grace overwhelm that just anger. The promise of a New Covenant is not that the old covenant would be restored. No. The promise is that He would make a New Covenant that would not be like the other covenants.
At this point (verse 32), the prophet returns us to the redemption of God's people from bondage in Egypt and the covenant made in the wilderness in order to show the contrast. The promise of the New Covenant will not be found in the law being written in tables of stone, nor with thunderings, lightening, and terror, nor through a weak mediator such as Moses. It will be written upon our hearts, with words of peace and consolation, through our only mediator, the Lord Jesus Christ. The weakness of the covenant made through Moses is shown in the breaking of it by God's people. The Lord was never unfaithful, yet the people were not inclined in their hearts to follow Him and obey Him. It was so bad, that the prophet speaks of the unfaithfulness of the people as harlotry (3:6-8) and worthy of divorce. Something needed to be done, and what was to be done is shown in verses 33 and 34.
In describing the New Covenant, four elements are described: 1) The law will be written on the hearts of His people. This is something that a human cannot do. No amount of skill can change the nature of the fallen human affections, inclinations and thoughts. That is the activity of the divine surgeon alone. 2) The Lord's people will be restored to their place of covenantal fellowship. All throughout redemptive history, God has promised to redeem a people to Himself. Now, the promise, in the form of the New Covenant, will be fulfilled in its completeness. 3) The Knowledge of the Lord will be widespread. This is not primarily a matter of the accumulation of data. The pervasive knowledge of the Lord speaks to both the extent as well as the intensity of knowledge. Under the old covenant, barriers were erected between the people and their God. In the New Covenant, those barriers are removed. 4) The final solution for sin and broken fellowship will be manifested. The answer to the problem is a person. It is our sins that drive us from God. It is sin that corrupts our knowledge and understanding of Him. It is our sins that cause a break in fellowship and peace with our fellow man. "But now once in the end of the world hath he appeared to put away sin by the sacrifice of himself. And as it is appointed unto men once to die, but after this the judgment: so Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation." (Hebrews 9:26 - 28)