A covenant is a solemn agreement. For example, marriage is described as a Covenant relationship in Malachi 2:14.
First and foremost, God enters into covenants with man. In the Covenant of Grace, God promises to be the God of His people in Christ Jesus.
In the Bible, we see people and nations responding by in-turn making covenants with God, particularly in times of crisis. Biblical examples of covenants are seen in Joshua 24: 16025; 2 Chronicles 15:12-15; 2 Kings 11:17; 2 Kings 23:1-3; 2 Chronicles 34:31, 32; Nehemiah 9:32, 38. And we believe that anything in the Old Testament not cancelled in the New still applies today.
In the Bible, even unwise covenants could not be cancelled unless it could be shown that what the people promised in them was wrong (see Joshua 9), or unless their aims had been fulfilled. And covenants also apply to the descendants of those who originally swore them (see this in practice in 2 Sam 21:1,2).