Simply put, "the woman" is the person with whom Willy has an affair. She is set up as a contrast to Linda, particularly in the way that Willy treats them both. Throughout the play, her flashbacks are juxtaposed with scenes of tension between Linda and Willy. For example, Willy gives her a gift of nylon stockings, which were a rare luxury for women during World War II, and it is the memory of this gift that causes Willy's pangs of guilt and anger when he sees Linda mending her stockings.
Her personality is also contrasted with Linda through her laughter. It serves as a piercing, shrill, painful reminder to Willy and Biff of Willy's infidelity. Willy's affair with the Woman is further evidence of his shortcomings, and illustrates how he has failed to live up to his own image of himself as the ideal husband and father.
"The Woman" is someone Willy is having an affair with. Her presence feeds into the theme of illusion vs. reality. Biff thinks the world of his father, but doesn't know until it's too late that his dad is cheating on his mom. "The Woman" has been forced to hide in the bathroom upon Biff's arrival because she is a secret herself. She is "hidden" from the rest of the family. She is completely different from Linda, the boys' mother. Willy buys gifts for "The Woman" like silk stockings, while Linda has to sew the holes in her own stockings.
"The Woman" is who Willy had an affair with. He cannot seem to get her off of his mind and always views the stockings as a part of the Woman. This is a constant reminder of his affair he had, and because of his affair, he drifted from Biff. His flashbacks mirror expectancy versus reality within the play.