One of the themes of Death of a Salesman is clarified by Biff in the Requiem. Based on his new understanding of life, his father, and himself that he has gained over the course of the play, Biff declares that Willy "had the wrong dreams" and that "he never knew who he was." Thus the play's message is that if one lacks a sense of identity, he will spend his life pursuing the wrong dreams. 

In the first part of the play, Biff plays along with Hap and Willy, proceeding on the assumption that he had been a top salesman for Bill Oliver, and that Oliver will be happy to see him again and advance him money for a business venture. But in Act Two, Biff has an epiphany after he steals Oliver's fountain pen. He asks himself why he is trying to become something he doesn't want to be, and then says, "All I want is out there, waiting for me the minute I say I know who I am!" When Biff realizes the connection between identity and pursuing the right dream, the dream that will bring true satisfaction, he becomes willing to look at himself objectively. He admits that he was never a salesman for Oliver--he was a shipping clerk. He admits he doesn't have what it takes to make it in business--that he's "a dime a dozen."

With this new understanding, he determines to make his father face the truth about his sons. He says, "The man don't know who we are! The man is gonna know! We never told the truth for ten minutes in this house!" He confronts Hap with his lie: He is not an assistant buyer, but an assistant to the assistant. He then pleads with Willy to burn his "phony dream" of Biff becoming ultra successful. Biff is unable to persuade Hap and Willy to look at their lives realistically and to create different dreams for themselves based on the truth.

After Willy's death, Hap embraces Willy's dream "to come out number-one man." But Biff has changed, saying "I know who I am, kid." This gives hope that Biff will not follow in his father's footsteps, pursuing a dream that is not based on his own true identity and therefore bound to fail. Biff's realization that he has been living a lie and his determination to face the truth underscores the theme that one can never reach satisfaction in life by pursuing a dream that is not grounded in the truth about who one is. 

Willy Loman is the central character in the play, but it is only Biff who sees the truth that Arthur Miller is trying to convey. Willy never does see the truth, which is that he is only a mediocre person with delusions of grandeur. Biff realizes that he has been injuring himself by trying to live up to Willy's unrealistic expectations. Biff tries to convey his new insight to his father but finds it impossible to communicate with him because Willy is just too old and too set in his ways to understand. Biff has a chance to start a new life because he is still young. It would seem that Happy, though still young himself, will not see the truth and will never change because he doesn't possess Biff's spirit or Biff's intelligence. Happy will go on trying to please his father even after Willy is dead. Willy must have been a good salesman to have sold himself so effectively to his wife and his two sons. 

One of the metaphorical deaths in the play is the death of the image Biff has of his father. He believes his father to be all powerful and infinitely strong. He travels to Boston to plead with his father to return to New York and get him out of the jam he is in. Upon discovering the woman in Willie's room, Biff immediately says that no one would listen to Willie. His image of his father is shattered and his personal dreams die. 

See the theme "Appearance versus Reality". 

I think that Biff's realization about his own life and the life of his father underscores the theme of the play in a couple of ways.  The fact that Biff himself is demonstrating some of the same harmful tendencies as Willy is significant.  Biff sees himself believing some of the same elements as his father and embodying the same level of self- hate as his father.  It is for this reason that his realization is significant.  It shows that Biff will not repeat the same mistakes that Willy has made in his life.  Additionally, I think that Biff's realization underscores the idea that the social construction of happiness and success as one intrinsic to wealth and the acquisition of wealth is flawed.  Biff recognizes what Willy cannot.  It is here where there might actually be some shred of redemption in the process.  Biff understands the need to change reality.  When he summarizes Willy's own life along with his own, it is a realization that cries out for a different conception of how to be happy:

You were never anything but a hard-working drummer who landed in the ash can like all the rest of them! ... I'm nothing, Pop. Can't you understand that? There's no spite in it any more. I'm just what I am, that's all.

It is here where I think that Biff's realization as to how he can live a different life than his father links to the theme of the drama.  Miller would not construct the characterization of men like Willy and Biff without seeing something in the world and recognizing the need to change it into what can or should be as opposed to what is.  Biff's realization is the illumination of this idea.  When he realizes it, a chance is developed for change.  It is here where Biff's realization underscores the theme of the drama.

One of the major themes of this play is the difference between appearance and reality.  The members of the Loman family have been scurrying to keep up the appearances of a well-adjusted and successful family when the truth is that Willy is no longer successful at his job, and Linda defends her husband and enables him to the point that she could allow him to kill himself.  Willy has lived an unfocused and unproductive life, haunted by the realization that his father was an adulterer while Happy hops from one woman to the next in his attempt to find the love and attention he didn't get from his parents.

Everyone attempts to keep up this appearance with horrific results.  Willy is finally pushed to the point of suicide.  At the grave, the absence of doting mourners is obvious, and Biff is finally driven to the epiphany, "We never told the truth for ten minutes in this house"  (Requiem). His avoidance of finding his father with another woman is finally released.  He understands his own drive to work on the land instead of in the business world and sets off to find it.  Unfortunately, his mother and brother remain in the same state of mind, hopefully NOT doomed to repeat Willy's fate.