God created Adam in a covenantal relationship with Him. We know this because Adam received commands and promises from God that would bless others; he represented others by his actions, whether for good or for ill; and the New Testament identifies Adam as the parallel to Jesus Christ, whom we know established God's new covenant in his blood. Adam's covenant was a covenant of works -- if he obeyed God's law, all would be well, if he broke the law, he would die. Adam broke God's law, so he and all of us died.
But God promised a Savior, a human being sent from the Lord who would destroy Satan (Genesis 3:15), thus undoing all that Satan engineered.
Then God gave a covenant of preservation to Noah, and through Noah to all of us. Never again would God destroy all the earth with a flood. The Lord appointed the beautiful rainbow in the sky as a sign of His mercy after the storm. Noah's covenant was a gracious promise, since God did not include any good-work conditions.
The next covenant God set up was between Himself and a Mesopotamian Gentile man named Abram. The Lord appeared to Abram, and promised him a land, a seed, and a blessing, all in perpetuity.
The land stretched from the Euphrates River on the northernmost end, to the Nile on the southernmost end. The seed was both physical and spiritual -- billions of physical descendants (of whom Jesus of the tribe of Judah is the most important), but he also has billions of spiritual descendants.The blessing was the lifting if death from the world.
The Lord unilaterally pledged to fulfill His promises. He put Abram into a deep sleep, then God's glory passed down the trail of blood three times, by Himself. Christ bled another river of blood on the cross, and that alone saves us by faith. Abram did no good works to earn this pledge from God. God chose Abram unilaterally and unconditionally, as an entirely free gift. And His pledge to Abram was permanent.
In Genesis 17, God added a sign of the covenant -- circumcision. This was an appropriate sign, since God was sanctifying a very particular family line to be His special people. Circumcision didn't save. Abram had already become a saved man years before, as described in Genesis 15. God in Genesis 17 created a new breed of people, the Jews. God's plan was to use these people to represent Him in the world, to the world.
Abram's covenant is the foundational covenant of the Bible. It shows the unconditional and unilateral nature of God's mercy. God did not approach Abram because Abram was a good man of good works. God simply chose to bless Abram because it pleased God to do so. Abram's covenant also reveals God's sovereignty. Abram had been an idol-worshiper from the land of Ur. He didn't choose God, God chose him.
This covenant shows God's saving plan for the world. Abram was a Gentile, and God promised to use him to bring the blessing to every family of the earth. But it also reveals the origin of the Jews, and shows the special commission to which God appointed them. If you are a Gentile who has trusted in Christ as your Savior, you can base your faith on God's Abrahamic promise to bless the nations. Jesus on the cross was how God kept His promise to Abram.
Abram's covenant is also crucial for assurance of your own faith. Abram's line is essential for identifying the true Messiah. The true Messiah must be a descendant of Abram. This is why the Gospel of Matthew begins with a geneology.
God's unconditional and unilateral commitment to Abram's seed proves that the Jews have not been set aside by God. The Old Testament prophecies of a glorious future for the Jews are based on the fact that God pledged Himself to Abram's seed. But Abram's ultimate seed is Jesus. God's promises to Abram are perpetual, but a Jew must trust in Christ to inherit them.
These reasons are why God's covenant with Abraham is the most important covenant in the Bible.