What is the promise in Genesis 3:15 about enmity between Satan and the woman's seed?
The promise is that God will put enmity between Satan and the woman, and between Satan’s seed and her seed. Galatians identifies the woman’s seed as Christ, so this is a running battle between Satan and Jesus Christ that begins immediately and continues as Satan tries to disrupt God’s plan.
Les explains that Genesis 3:15 does not mean much unless you know the rest of Scripture. Galatians tells us that the seed of the woman is Christ, so what is really promised here is a running battle between Satan and Jesus Christ, and it is seen from this moment on. Just as soon as Satan understands God’s particular program, he comes in and tries to disrupt it. After God made the covenant with Abraham, Satan began a process that has been running for over 4,000 years to destroy the nation of Israel, because God promised that everything would be fulfilled through that little nation. If Satan could destroy the Jew, then he thwarts God’s plan for the ages. So everything begins right here, this running battle. The passage then moves to verse 17, where God speaks to Adam and curses the ground and all creation.
And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.