How does Jesus fulfill the Protoevangelium (First Gospel) in Genesis 3:15? In the judgment of the serpent in Genesis 3:15, God says the following:


  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.  Genesis 3:14-15 ESV


Verse 15 has become known as the Protoevangelium, or "First Gospel".  How is this the first gospel and how does Jesus fulfill this prophecy?
Gospel means &quot;good news.&quot; Understood rightly, this bit of news to Adam and Eve was certainly good news. The snake - the epitome of sin - had tricked Adam and Eve. Because of the snake (and their own sinful actions, of course) they were being kicked out of the garden. By trying to become like God, they had become like the snake - sinful and evil.
But God promises to put enmity between them and the snake. He would pull them apart from their wretched connection to sin and death. How?
A savior. A promise. Importantly, not Adam. Adam and Eve weren't going to get themselves out of this mess. Their offspring would. An offspring who would be born through the humiliating and painful process that God had just described to Eve a few verses back (the curse of the pain of childbirth). An offspring who would be injured by the snake (crushed on the heel) but who would, ultimately, crush the head of the snake.
What makes this the first gospel is of course the gold mine of promise beneath the metaphorical literary layer. The offspring of Eve would destroy the snake who brought Adam and Eve to sin and death, and in doing so separate them from that sin and death. He would undergo pain in the process, but it would be a trivial wound (on the heel) versus the mortal blow on the head.
Jesus was Eve's offspring, naturally. He was born to a virgin, was the son of a carpenter, born in lowly Bethlehem, placed in a manger, and raised in despicable Nazareth. He was born in a state of humility.
He was despised. He was beaten. He was killed on a Roman cross, the death for traitors and murderers. He temporarily went through Hell for his people. Satan had indeed bruised his heel, but that death had paid for the sins of his people.
And when Christ rose from the dead on the third day, he conquered death. He conquered the very thing Satan had brought into the world and brought back Adam and Eve to himself.

For as in Adam all die, so in Christ shall all be made alive. 1 Cor. 15:22