A covenant is a legally binding agreement between the two parties used in the Bible as a metaphor to describe the relationship between God and His people. It was practiced in the most ancient cultures which indicates that the concept of covenants began in Genesis 3 after the fall of man with the promise of a Redeemer.
In the form it was made in ancient cultures between men, it was a binding and solemn agreement between two or more parties. There were different kinds of covenants in the biblical world, and one of those types of covenants, the "royal grant", was similar to the Biblical covenants where God, the superior party binds Himself to be the beneficiary as an inferior party with no set conditions imposed upon him. In this type of "royal grant" covenant, a king or other person in authority rewards a loyal subject by granting him an office, land, exemption from taxes, or similar.
Such covenants are also referred to as covenants of promise or unconditional covenants. The covenants God made with Noah (Genesis 9:8 - 17), Abraham (Genesis 15:18), and David (2 Samuel 7; 23:5) fit this pattern. In each of these cases, it is God alone who binds himself by a solemn oath to keep the covenant.
The Mosaic covenant (Ex. 19 - 24; Deuteronomy; Joshua 24) is like another type of ancient covenant, the "political treaty" between a powerful king and his weaker vassal. Following the standard form of such treaties, God, the suzerain, reminds Israel, the vassal, how God has saved it, and Israel in response accepts the covenant stipulations. Israel is promised a blessing for obedience and a curse for breaking the covenant.
These two different conceptions of covenant, one stressing promise, the other obligation, eventually modified one another.
The Covenant which Yeshua instituted with Israel is a culmination and inclusion of all the other covenants in a renewed form in which all the promises are made available in the Messiah through the power of God and man is the recipient of these benefits.