14 The LORD God said to the serpent, "Because you have done this, cursed are you above all livestock and above all beasts of the field; on your belly you shall go, and dust you shall eat all the days of your life.
15 I will put enmity between you and the woman, and between your offspring and her offspring; he shall bruise your head, and you shall bruise his heel."
The man, the woman, and the serpent all suffered consequences as a result of their part in the disobedience against God. This is the serpent's curse, which is far worse than that of the man and woman, a prophecy and a promise from God.
The promise is that the offspring of the woman will strive with the serpent (who is Satan). However, the serpent will only bruise his heel, but the offspring will bruise the head of the serpent. This is widely accepted as a prophecy about the Christ to come who will eventually defeat sin and undo all of the effects of the fall.