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The Covenant of Grace
The Abrahamic Covenant is really the beginnings of the formal revelation of the covenant of grace, of God's decision to reach into humanity and specifically save people for Himself. It comes in the form of a promise to Abraham. Abraham, who's the son of an idolater, who did not know God. God takes the initiative with him, calls him into a relationship with Himself, and makes just unilaterally some promises to Abraham. He promises that Abraham is going to be a great nation, that he is going to be given a land, a place to live, and that through Him, all of the nations will be blessed.
Now that promise that's given in Genesis 12 takes on a very formal, a covenantal form, later on in Genesis, in which God reaffirms the promises and takes an oath, basically makes a lasting promise to Abraham that He will not fail to come through on this.
Origins of Covenant
Normally, when a covenant was made in the ancient Near East, they would talk about the covenant being cut. The cutting of the covenant involved the sacrificing of animals. Animals would be literally cut in two. The person who had to keep the promises would walk through those animals, basically saying, "If I don't keep my end of the bargain, may be done to me what has been done to these animals." Typically, in a covenant, the great king would force the lesser party in the covenant to walk through those animals. It was up to the junior member of the party to keep the terms of the covenant.
What's so amazing in the Abrahamic Covenant is that God Himself takes the threatened curses upon Himself, guaranteeing, as He walks through those animals that are cut in two, that He will certainly bring this promise to pass.
Later on, in Genesis 17, the promise is given a specific sign with the sign of circumcision. Abraham and his son, Ishmael, are circumcised, making clear that they and all of their household are set apart to the Lord. This covenant, this promise, of blessing to Abraham, to Abraham's seed, and then to the nations through Abraham really is the beginning of the covenant of grace that's going to find its fulfillment in Jesus Christ.
3 Tenets of the Abrahamic Covenant
1. To make of Abraham a great nation and bless Abraham and make his name great so that he will be a blessing, to bless those who bless him and curse him who curses him and all peoples on earth would be blessed through Abraham.
2. To give Abraham's descendants all the land from the river of Egypt to the Euphrates. Later, this land came to be referred to as the Promised Land or the Land of Israel.
3. To make Abraham the father of many nations and of many descendants and give "the whole land of Canaan" to his descendants. Circumcision is to be the permanent sign of this everlasting covenant with Abraham and his male descendants.