One of the most influential scenes is act 2, scene 3, which is where Willy goes to Charley's office and ends up talking to Bernard, Charley's son.

This scene is important because this marks the first time that Willy takes a serious look at what his son Biff's life has become and the reasons why Biff's life took a turn for the worst, leaving Biff lost basically forever.

Remember that all this time, Willy has lived in a formulaic way that clearly does not work for anyone. He goes by the tenet that being well liked and popular is all you need to succeed. He also erroneously believes that he is doing right by staying in a job that does not pay and that he can no longer do. As such, he also remained stuck in his fantasy that Biff, his "Adonis-like" son, has all the tools he needs to succeed "if only he cared enough."

In this scene, Willy finds out via Bernard that Biff's life became shattered when he found out that Willy was cheating on Linda with "the woman" that Willy spent time with at a hotel during one of his trips. During a surprise visit to see his father, Biff finds all of this out. It was as if the only mentor Biff ever had, which was Willy, had come down from a pedestal, showing Biff along the way how everything Willy ever taught Biff was advice based on magical thinking and ridiculous expectations.

Once Biff realizes all of this, his dreams shatter and he feels so lost he decides to leave, presumably to find himself again. However, we know that this really does not happen. Biff is aware of the empty legacy left behind by his father and recognizes his responsibility in needing to turn his fate around.

I'm surprised that no one has yet mentioned the scene in which the title of the play is mentioned.  Willy goes to Howard's office to convince Howard to give him a raise and to take him off the road.  Howard thinks that Willy, like all others, should pull their own weight in the business.  He isn’t concerned with Willy’s plight—all that matters to him is money and business.  Willy tells Howard about Mr. Singleman, the ultimate salesman, who died a respectable death and was remembered and well known throughout his district.  Willy is in a dreamy state here as he recalls this story, suggesting to the reader that he in fact wants to live a life as a well-known and respected person.

Different interpretations of the word "important" play a part in answering your question. That said, consider these two scenes from the play. The scene in Willy's Boston hotel room is important because it explains a great deal about Biff's unfocused life, his continuing hostility toward his father, and Willy's repressed guilt. When Biff finds his father with the woman in the hotel room, Biff's respect for his father is shattered and their relationship is...