The focus, the central point, of Genesis 3:15 is that the seed of woman, the Lord Jesus, would come to destroy Satan on the cross. This is the strongest proclamation in the preaching of the glad tidings. Once again I say that Adam and Eve were trembling under the imminent sentence of death, but God, instead of condemning them, surprised them by preaching the gospel to them. Adam and Eve had fear toward God and hate toward the serpent. Therefore, God declared in His glad tidings that One entitled "the seed of woman" would come to destroy the serpent. That was the gospel. The promise regarding the seed of the woman and the coming destruction of the serpent was the glad tidings proclaimed to the first generation of sinners.
The promise of Genesis 3:15 has been fulfilled throughout the generations. Firstly, it has been fulfilled in all the people of God. From the time that this promise was first given Satan has been the enemy of God's people. He will continue to be their enemy until he is cast into the abyss (Rev. 20:1-3) and ultimately hurled into the lake of fire (Rev. 20:7-10). Until Satan is cast into the lake of fire he remains the enemy of the people of God.
Furthermore, this promise is fulfilled in all the overcomers until the time of rapture. This is revealed in Revelation 12.
This promise has been completely fulfilled in the Lord Jesus. Firstly, it was fulfilled at the time of His birth (Matt. 2:13-22). When the Lord Jesus was born, the serpent stirred up a great deal of enmity, causing many young lives to be lost. Secondly, the promise was fulfilled throughout the Lord's earthly life. If we read the four Gospels, we will see that Satan was continually troubling the Lord Jesus, pursuing Him and opposing Him. Eventually, Satan bruised the Lord's heel on the cross, as was prophesied in Psalm 22:16.
The promise in Genesis 3:15 reveals that Satan is the enemy of the people of God. Eventually, the Lord Jesus came as the seed of woman to destroy the enemy. Today we are enjoying the fulfillment of this promise.