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 is a curse on the serpent for deceiving the woman into eating from the tree of the knowledge of good and evil thereby causing her to become a sinner. Many theologians think that when Adam took the fruit from Eve and also ate it that they died spiritually. Initially the first pair were innocent but without eternal life since eternal life is symbolized by the Tree of Life (see Rev. 2.7b, 22.2,14,19). Now however, their sin nature was evident since they hid from God when He visited them. All Adam’s and Eve’s offspring also subsequently share their progenitors’ fallen nature: 

“As for you, you were dead in your transgressions and sins, in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient. All of us also lived among them at one time, gratifying the cravings of our sinful nature and following its desires and thoughts. Like the rest, we were by nature deserving of wrath.” (Eph. 2.1-3 TNIV)

God in His grace clothed Adam’s and Eve’s nakedness and cursed the serpent (not snakes per se but the entity behind this particular serpent: the devil). The curse formula is given in somewhat cryptic terms but Satan was aware that his head would someday be crushed by a human supernaturally born of a woman. Satan, it is thought, searched out aspects of this divine human in the scriptures so to thwart the Messiah in some way. during Christ’s temptation, the devil quoted from Psalm 91:  Then the devil took him to the holy city and had him stand on the highest point of the temple. “If you are the Son of God,” he said, “throw yourself down. For it is written: