that her actual identity did not, and still does not, matter to Willy. The audience is left to decide if he even remembers her name. If not, given that he retains dozens of minor details from the past, his forgetting accentuates her lack of importance.

What is significant is her function in representing the flimsy, unstable foundation of Willy’s marriage and family. He pretends to care about being a good provider and role model, but when he had the chance, he was unfaithful to his wife. Even more than his betrayal of Linda, the scenes with the Woman are important because they expose Willy’s hypocrisy as a father. Once Biff discovers that his father is not the man he thought he was, his trust is shattered. It devolves to Biff to keep the secret and protect his mother, with the consequence that she can never understand or accept his disdain for his father.

"The Woman" first appears in act one of the play. Willy is speaking with his wife, Linda, but a moment from his past (and specifically from his extramarital affair with "The Woman") intrudes upon his present. At first Willy hears the laughter of "The Woman" and tries to talk over it, perhaps to prevent his wife from hearing it or perhaps in an effort to defeat and suppress the memory.

The moment when the memory overcomes the present coincides with the moment when "The Woman" says to Willy, "I picked you." Willy is so pleased to hear her say this. In fact, he is almost incredulous, asking her twice to affirm that it is true. The fact that "The Woman" chose him gives him a sense of validation that he is increasingly unable to achieve in his present reality. "The Woman" is thus significant because she helps us to understand, by way of contrast, what Willy lacks in his life in the present.

"The Woman" is also significant because she changes our emotional reaction to Willy. The discovery that he once had an extramarital affair perhaps reduces the sympathy which we might otherwise feel for Willy. Alternatively, Willy's affair with "The Woman" might actually increase our sympathy with him, if we interpret it as just another manifestation of his abject loneliness.

Another reason as to why "The Woman" might be significant is because we can infer that she—or rather, the affair that Willy had with her—is likely a cause of guilt and shame for Willy. This might help explain why he is so insecure, and it also might help explain, at least in part, his psychological breakdown.

The second appearance of "The Woman" is in act 2, when Biff discovers her and his father in a hotel room together. This moment is very significant because it explains so much about the fractious relationship between Willy and Biff. This is the moment when Biff stops idolizing his father and instead sees him as a liar. He yells at his father, "You fake! You phony little fake! You fake!"

In this moment, Biff loses his role model, and, at the same time, he loses his own identity. His own identity, after all, was made very much in the image of the man he thought he knew. "The Woman" is significant, therefore, not only because she helps us to understand Willy, but also because she helps us to understand Biff.

"The woman" is a woman in Boston who Willy had an affair with when he was a travelling salesman and his sons were in high school. Read more on "the woman" on eNotes here. 

In the play, Willy's infidelity is revealed through flashbacks, and his guilt is symbolized by stockings: Linda works hard to mend her stockings because Willy can't afford to buy her new ones, but he once bought a pair of new stockings for his mistress.

Later in the play, it is revealed (through flashbacks) that Willy's son Biff discovered his affair. That's what made Biff lose faith in his father and forget his dreams and ambitions. So since Willy's depression is caused by his son's failures as well as his own, the audience could blame his affair with "the woman" for all his problems.

Why did Willy have an affair, then? Willy always considered popularity to be the hallmark of success. Throughout the play he insists that he is "well-liked." The attention of another woman made him feel well-liked, and therefore successful.

However, it also led to his feelings of extreme guilt, partly because he cheated on his wife who has always loved and supported him, and partly because his affair caused his son's downfall.

It could be said that "the woman" represents poor choices or bad decisions. If Willy had been able to resist the temptation to have an affair with an adoring young woman, perhaps Biff would have retained his admiration for his father and gone on to succeed in college and his career, and perhaps Willy would not have felt so ashamed of himself and been a better salesman, or been able to keep up with the changing times and get on with his life after getting fired. 

Symbolically, the woman Willy sleeps with in Boston represents Willy's moral failure. 

Despite his repeated pronouncements that a person must have character to succeed in life, Willy demonstrates a clear lack of integrity by having an extra-marital affair. 

We see a few important elements of Willy's character in this contradiction. First, Willy is a dreamer who does not seem capable of truly dealing with reality. He refuses to face up to what he has done and, instead of asking Biff's forgiveness or Linda's forgiveness, he denies the facts and Biff moves out of the house. 

In this denial of the facts of his wrong-doing and moral failure, we see Willy's moral weakness. While he has some talents, some charm, and some other admirable qualities, Willy is essentially incapable of doing difficult moral work. He cannot admit his guilt.

This guilt is symbolized by the woman in Boston.