What does the promise in Genesis 3:15 mean for the conflict between Satan and Christ?

The promise in Genesis 3:15 establishes enmity between Satan and the woman’s seed, and Galatians identifies that seed as Christ. It therefore announces a continuing conflict—a running battle—between Satan and Jesus Christ, starting from that moment, as Satan attempts to disrupt God’s program.

Les teaches that Genesis 3:15 is not merely a statement to Satan; when understood with the rest of Scripture, especially Galatians, the seed of the woman is Christ. So what is really given is a promise of 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 running 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, he would thwart God’s plan for the ages. This running battle begins right here.

Genesis 3:15

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.

What does it mean that Satan would bruise the heel of the seed of the woman?

It means Satan would cause the suffering that Christ, the seed of the woman, had to endure for our salvation. Christ would crush Satan's head through His death and resurrection, defeating him, but Satan would still bruise His heel by inflicting suffering.