The lady that tempted Sir Gawain is Bertilak’s wife – Lady Bertilak. For three days in a row, she attempts to seduce the knight. However, she only receives several modest kisses. This scene has a full-page depiction dedicated to it in the oldest surviving manuscript of the poem.
Detailed answer:
After striking a deal with Bertilak, the knight stays at the court. While being in the castle, Gawain manages to obtain kisses from Bertilak’s wife. He exchanges those kisses at the end of each day for the game that the host hunted down. The lady comes into the knight’s room every day to tempt him. Yet, every time, the knight rejects her. Every attempt at seducing Gawain is performed in a mix of debate and smooth talking, in which lady Bertilak seems to be dominating over the guest.
Her primary role in the story is to present Gawain with an option to save his life. The lady has a green girdle, which is able to protect its wearer from death. The hostess tells Gawain about the girdle after asking him for a token of love. Hearing about it gives Gawain hope to survive the encounter with the Green Knight. This is all a part of Morgan le Faye’s plan to trick the knight into giving up his honor and teaching him a lesson.
Even though the lady is just a pawn in the hands of the great sorceress Morgan le Faye, she stands out as an intelligent woman. In every dialogue with Gawain, she presents a strong ability to read his thoughts and predict his responses. This means that, on top of being a beautiful woman, she is also a brilliant debater. It is not hard to see why Morgan chose her to perform the wicked plan.