Biff travels upstate to surprise his father, & finds another woman in his hotel room. The shock of the adultery, in addition to the feelings of betrayal and abandonment, drives Biff throughout the rest of the play. He is consumed by his father's failings, which translate into his own inability to "settle down"- he lacks a steady job, & his relationships with women are disastrous. Even his relationship with his mother is destroyed; he loves her, & wants to protect her, but he is driven to rage by her defense of Willy. Thus, when she sticks up for her husband, Biff reacts with anger and shouting.
When Biff fails math, he immediately runs to his father. Willy has always told Biff that he is special, that his athletic ability and his good looks are all that he need. Biff believes that the grade won't "count." He thinks that Willy will be able to intervene and convince the teacher to pass him.
Biff meets up with Willy in Boston. However, when he gets there, he finds Willy with his mistress. This destroys Biff's image of his father. He screams at his father,
"You fake! You phony little fake! You fake!”
Discovering that his father is a fake makes Biff question all that he believes about himself. Biff's self-image has been built up by Willy - the destruction of Willy has therefore destroyed Biff's self-image. He goes home and burns the sneakers on which were written the "University of Virginia." He refuses to take the summer class, mostly because he no longer has the goals that Willy had helped him establish, but also in part because Willy orders him to - he will no longer do what Willy "orders" him to do. Finally, he goes off in search of his own life path.
Biff in the current time of the play is the Biff still looking for that life path, and still trying to understand a father that had disappointed him so much.