Because of Christ's atoning sacrifice, everyone—Jew and Gentile—could receive the same blessing that Abraham received. Part of that blessing, which began all others, was justification by means of faith rather than by works. God knew, from the foundation of the world (when Adam and Eve sinned and started this present order of things), that justification by works would not be possible. It is not possible for a man to keep the entire law (letter and spirit) without having the same Spirit as the Lawgiver. Abraham, the father of the faithful, showed that the way to justification was by faith in what God is doing and will do, rather than on our own goodness. These same blessings that Abraham received (justification, God's Holy Spirit, the sanctification process, spiritual gifts, and future glorification) are available to anyone else that God has called, regardless of their race, social status, gender, etc.
God's promise to Abraham (Abram) is detailed in Genesis 12:1-3. Part of that promise was that "in you [Abraham], all nations of the earth would be blessed." Later, in Genesis 13:15, God expanded the promise to include eternal life too—the only way it is possible for Abraham (and his descendants) to have the land "forever" is if Abraham was to be living forever. Land is worthless to the dead.
John 17:3 defines eternal life: "And this is life eternal, that they might know you the only true God, and Jesus Christ, whom You have sent." Eternal life is knowing—experiencing—God. But God does not allow just anybody to know Him; it is evident from John 6:44 and other verses that God must call someone to a relationship with Him. A man cannot, of his own volition, initiate a relationship with God—Abraham's life shows this clearly.
Mankind had the opportunity through Adam and Eve to have eternal life, but once sin entered the world, and death through sin (both of which are the antithesis of God), God had to guarantee that He would not have sinful beings living forever. God blocked the way to the Tree of Life with a flaming sword, and since that time the only way to approach the Tree of Life has been through God's intervention and calling.
When God calls a person and makes a relationship with Him possible, it is through the atoning blood of Jesus Christ. The person must first be justified before God, and the only way that justification is possible is through faith in Christ. Once a man is justified, God then gives a measure of His Holy Spirit to him. If a man completes the sanctification process, by means of yielding to the Holy Spirit, upon resurrection or Christ's return that man will be changed into a spirit being and live forever with the rest of the God Family. All of this is a fulfillment of the promise that God gave to Abraham and to his Seed.