that he's been fired. Biff can't bring himself to add to his father's misery by telling him the truth about the meeting. So, instead, Biff lies to his father. He tells Willy that Bill Oliver is considering making an investment and is talking it over with his partner. 

People often talk about Death of a Salesman as a play that reveals the American dream to be a dangerous myth. In this reading, Willy Loman is the victim of a false promise: the promise of success in a country rich with opportunities.

But, as the subplot with Bill Oliver suggests, family members play an important part in preserving the myth of the American dream. The play shows how family members hide from each other the fact that failure in America is not only possible, but common. Sometimes the family members do this out of selfishness or pride, and sometimes they do this out of love or worry. The subplot involving Bill Oliver raises important questions about the ethics of telling the truth, when it is kind, and when it is not, and shows how family relationships are one mechanism by which the American dream is perpetuated. 

As the previous answer states, Bill Oliver is a former boss of Biff's. Biff has never been able to settle down long to any job, but he seems to hold out a hope that Bill Oliver might lend him money because he was a favorite employee of his. Happy conceives the idea of a starting a business partnership with his brother, and the money from Bill Oliver would enable them to set up that business.

However, the idea of a loan from Bill Oliver is just another pipe dream of the Lomans', and comes to nothing when Bill Oliver doesn't even remember Biff when he goes to see him. As the previous answer states, this is really the moment when Biff realizes once and for all that his life has just been a "lie"; he was never actually a big salesman for Oliver, as his father Willy likes to pretend, but a lowly shipping clerk:

We've been living in a dream the last fifteen years.

Whatever Willy might say, Biff is painfully aware that his career thus far has been a complete shambles and that he's simply not cut out for the kind of high position in the business world that Willy is always dreaming of. All he has really done is replicate his father's failures. The fiasco with Bill Oliver precipitates the final, fateful showdown between Biff and his father. 

Biff is locked in a cycle of deception and dysfunction in his life and his relationships with others, particularly his father. He has come back home after a failed attempt to live away from his father, mother, and brother. Despite his dislike of the city and office work, he allows his brother and father to talk him into seeing a former employer about a loan he can use to start a sporting goods business. In Act I the family, including Biff, imply that Biff formerly worked as a salesman for Bill Oliver. 

In Act II, Biff reveals he has spent the entire day in the reception room at Bill Oliver's office. After waiting six hours and even trying to flirt with the secretary to get an appointment, the man finally appeared at 5 p.m. Bill Oliver didn't even remember who Biff was, and he only spoke to him for about a minute. Biff found himself all alone in the waiting room. For some reason, he compulsively entered Oliver's office and stole his gold fountain pen. He realized he had never been a salesman for Oliver's company; he had merely been a shipping clerk. It dawned on him "what a ridiculous lie my whole life has been." After Biff stole the fountain pen, he ran out of the office and down eleven flights of stairs.

During the dinner at the restaurant with Hap and Willy, Biff tries to explain the situation, but Willy begins to lose touch with reality. Biff vacillates between making up a better story and telling the truth. He also reveals that in the past, presumably when he was employed by Oliver, he had stolen a box of balls from the company. Now having stolen from the man again, he can certainly never go back to speak to him about anything, let alone a loan of $10,000. Later he reveals that he "stole myself out of every good job since high school." However, stealing the fountain pen creates an epiphany for Biff. He looked at the pen and asked himself, "What am I doing in an office, making a contemptuous, begging fool of myself, when all I want is out there, waiting for me to say I know who I am!" Through this experience, Biff is finally able to look at himself and his life honestly.