Genesis 3:15 says, 'And I will put enmity between you and the woman, and between your seed and her Seed; he shall bruise your head, and you shall bruise His heel.' This verse first speaks of the adversarial relationship (enmity) between Satan and women in general. He particularly hates women, as can be seen in the way women are subjugated and mistreated throughout most of the world. Only Israel and the Christianized nations have elevated women to their biblical place of honor. Yet even in those places the adversary attacks women with abuse, prostitution, pornography, and abortion.
Next the verse speaks of the enmity between between Satan's seed and the woman's Seed. Satan's seed represents the adversaries of the true God. For example, in John 8:44 Jesus says to a group of Pharisees, 'You are of your father the devil, and the desires of your father you want to do. He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him.' These are undoubtedly some of the men who instigated the execution of Jesus. Later, in Acts 13:9-10, Paul confronts a man named Elymas who was trying to prevent him from speaking to Sergius Paulus about the Lord. The Bible says that Paul, 'filled with the Holy Spirit, looked intently at him and said, 'O full of all deceit and all fraud, you son of the devil, you enemy of all righteousness, will you not cease perverting the straight ways of the Lord?' These are two biblical examples of the seed (or children) of Satan. Keep in mind that in the Bible, to be a child of someone does not necessarily mean you are the literal child of that person; it can also mean you are like that person. To be a child of the devil means you are acting like the devil.
As for the Seed of the woman, clearly this is a reference to the Lord Jesus. For 'when the fullness of the time had come, God sent forth His Son, born of a woman' (Galatians 4:4). In contrast to the children of the devil, Jesus is literally the child of a woman.
Genesis 3:15 then concludes that the woman's Seed 'shall bruise your head, and you shall bruise His heel.' In other words, Satan will inflict a painful but non-fatal wound on Jesus, while Jesus will inflict a mortal wound on Satan. This is exactly what happened on the cross. Hebrews 2:14 says, 'Inasmuch then as the children have partaken of flesh and blood, He Himself likewise shared in the same, that through death He might destroy him who had the power of death, that is, the devil.' But as we know, the death of Jesus on the cross was not final, but was overturned by His resurrection from the dead. The Seed of the woman now stands triumphant while the devil stands condemned.