Gawain shows loyalty to his uncle, King Arthur, when he is the only one to step forward to accept the Green Knight's challenge. The Knight had urged any of the Knights of the Round Table to take his ax and attempt to decapitate him. None of the Knights of the Round Table (Arthur included) took him seriously, so no one came forward. When the Green Knight insisted, only young Gawain, not even yet a knight, came forward to save face for the knights of Camelot. Before taking the Green Knight's ax, Arthur knights Gawain in a brief ceremony. Once Gawain cuts off the Green Knight's head, the Green Knight's body picks up his own head and declares that he will see Gawain in one year so that the young man can receive the return blow that is coming to him. Gawain is determined to follow through with his part of the bargain in order to show his loyalty to Arthur and the Knights of the Round Table. He sets out, and eventually does face the Green Knight on New Year's the following year.
He also shows loyalty to the lord of the house when they exchange each day's hunts.