Critics identify several characteristics of a medieval romance, and Sir Gawain and the Green Knight fulfills these characteristics in several ways. I would like to focus on the following main characteristics:
1. Medieval romance usually idealizes chivalry
The concept of chivalry relates to the behavior of knights and their treatment of women. Knights were expected to show the highest level of respect for women including maintaining their chastity and showing a reverence toward them indicated of the Christian love for the Virgin Mary. They would should this reverence by dedicating their battles to a particular lady, perhaps representing her family colors in doing so. Gawain shows this for the Lady of the castle in that he denies her sexual advances without hurting her feelings, refuses her expensive gifts which he cannot repay and accepts her green scarf as he rides into battle.
2. Medieval romance idealizes the hero-knight and his noble deeds.
The hero-knight is expected to show unparalleled loyalty for his king, honesty in all areas and bravery at the face of death. Gawain exhibits all three. First, he accepts the challenge of the Green Knight when nobody else will except for Arthur himself. This challenge involves basically traveling to the Green Knight's home to receive a blow to the neck - certain death. While at the Lord's home, he does not lie about his kisses with the wife, but instead returns them as promised to the Lord. Even when presented with a plan avoid certain death, he keeps his promise of meeting the Green Knight. Finally, he accepts not one, but three blows to fulfill his obligation to the Green Knight.
Ultimately, Gawain shows his level of nobility by his level of self-hatred upon what he perceives as failure. He keeps the sash for personal reasons and does not give it to the Lord. This shows his fear for his own safety. Even though King Arthur, the knights and the Lord all forgive him for this, he still sees himself as a failure. In a way, this is how the work shows its comment upon how the level of behavior that knights are expected to uphold may be unrealistic.