Gawain wears the green girdle that was given to him by the Green Knight to show his shame. He shamefully lied to the Green Knight even though the knight knew the truth all along. Gawain is left to wear the girdle as a symbol of his shame.
This relates to the theme of reality and responsibility, as well as maturity and adulthood, as both groups that were forced into these inhospitable, frightening, and confusing circumstances were comprised of people who were or were barely more than kids.
