The Green Knight shows up in King Arthur's hall and offers to play a game. After none of the knights offer to take the Green Knight's challenge, King Arthur offers himself.
Sir Gawain offers himself in King Arthur's place. He realizes that he has to uphold King Arthur's reputation as having a mighty, fearless army.
The Green Chapel
The Green Knight allows Sir Gawain the first hit at his neck. Sir Gawain cuts the Green Knight's head off on the first try.
Next November, Sir Gawain travels to the Green Knight's chapel to uphold his part of the challenge. Along the way he meets a man who lets him stay at his castle. While he is there, his wife gives Sir Gawain a green sash that will protect him.
Sir Gawain makes it to the Green Chapel where the Green Knight is waiting for him. He is ready to take part in the challenge and uphold his promise.
The Green Knight isn't able to cut Sir Gawain's head off. This makes Sir Gawain victorious, and he wins the Green Knight's axe.