A covenant is a contract or a binding agreement. As God can not lie or break his promise, covenants are vital to showing that God keeps His word.
The first time a covenant was mentioned was between God and Noah in Genesis 6:18. God intends to wipe out every living thing from the earth except Noah and his family. This was fulfilled by God preserving Noah his family and the animals on the ark through the flood.
The next covenant is between God and Abraham, commonly known as the “Abrahamic Covenant”. This is in regards to the land that God will give Abraham and his descendants through Isaac and Jacob. This was fulfilled with Moses leading Israel to the promised land. (Exodus 2:24)
The Davidic Covenant is in regards to Jesus ruling from the throne of David which will be fulfilled in the Millennial Kingdom.
These promises from God are eternal and can’t be changed as there was no conditions put on the contract for Noah, Abraham or David to do, God just says what He will do. There is also the Mosaic Covenant which is conditional on Israel obeying the Law that God handed to Moses to bring to Israel. If Israel obeys God’s commandments, God will bless them. If they don’t, God will take away what they have. We know from history that after Solomon, Israel had a civil war and the kingdom split in two. The Northern Kingdom slipped into idolatry and fell to the Assyrians. The Southern Kingdom lasted 100 more years, but eventually fell to idolatry as well and were taken captive in Babylon despite the warnings from Jeremiah.
Jeremiah 31:31 states:
31 Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah:
The book of Hebrews points out that Jesus is the New Covenant as Jesus is the fulfillment of the Law.