A Covenant is a formal agreement between 2 or more parties committing to a particular relationship. The most common one people talk about being, 'The Marriage Covenant'.

God amazingly in spite of our flaws, chooses to be in a covenantal relationship with humanity, a relationship very much like a marriage. In many ways, and in places in the Bible he indicates that he views it as a marriage. The problem is that his marriage partner is a human being. Israel repeatedly cheated on Him and we humans keep messing it up, finding endless new ways to cause 'cracks' in God's good order and stuff up His creation (both the planet and ourselves). Each time the covenant with God is broken, you let death, division and disorder enter the world. God has to 'cover over' the crack, 'cover' is the Hebrew word for 'atones' and He has to restore the relationship in a new covenant, and He launches some form of new creation.

It happens after the flood, with a whole new creation. It happened with Abraham where the family of God was created. It happened at Mt Sinai where the people of God were created. It happens with David, when the kingly line is created. Sadly reading through Israel's history and the prophets the same patten repeats and repeats, covenant, disobedience, curse, God's gracious atonement for us, new covenant, new creation.

While God's grace is astounding, the repetitiveness is depressing. Humans keep messing things up, repeatedly releasing chaos in our world. Will God eventually run out of patience? I don't think so, it is not how many times you fall, it is how many times do you get up again. Which is not to say that he won't take action. But even in the darkest times of the prophets, God promised a New Covenant would come: the Covenant of Peace.