The conflict between these two characters stems from the discovery that Biff makes about his father and his extra-marital relationship with the woman from Boston, whose memory dogs Willy throughout the play. You might like to analyse this conflict by comparing the relationship that Biff has with his father when he is a child, and then the kind of relationship he has with him when he is an adult.
As a child, Biff clearly idealises, loves and looks up to his father. This is because he has swallowed whole Willy's creed that success is possible in anything if you but work hard enough at it. However, as an adult, we see that Biff's relationship with his father is characterised by disillusionment and cycnism, as he has been forced to accept that not only his own life is a failure, but his father's life is also a failure too. Consider what Biff says with considerable perceptiveness when they are talking about how the company think about Willy:
I don't care what they think! They've laughed at Dad for years, and do you know why? Because we don't belong in this nuthouse of a city! We should be mixing cememnt on some open plain--or carpenters. A carpenter is allowed to whiste!
Biff recognises something that Willy is unable to see. Because of who they are and the kind of talents they possess, the Loman family should not be trying to live their life in an urban environment. Instead, they should be in the countryside working in a trade. It is Willy's inability to drop his implicit faith in the American Dream that therefore creates the conflict with his son. Willy lives the American Dream to the absolute full and he is unable to understand why his son has dispensed with this creed, which, as Biff rightfully recognises, has only brought his father and himself sadness and despair.
In Arthur Miller's Death of a Salesman we encounter an ongoing conflict between salesman Willy Loman and his eldest son, Biff. The conflict stems from Willy's parenting philosophy and his philosophy of life, as a whole. In his eyes, the key to success in life is to be well-liked, attractive, and basically outsmart everybody around you.
He bestowes this philosophy onto Biff as he grows up. Biff becomes a High School football hero. This is reason enough for Willy to believe that he and his son are in tandem: He believes that they are both working together towards a similar goal- to be liked, to be feared, and (with that) to be successful.
When Biff fails Math in his Senior year, he hinders his future college career, bringing all his hopes down. Furthermore, he discovers during a surprise visit to his father that Willy is having an affair. This brings down the idolatry and trust that Biff has in his dad. From that moment on, Biff realizes that his life has only been a continuation of Willy's fantasies, and this is their basic conflict: While Willy strongly holds on to his dreams, Biff is desperately looking for a way out of Willy's fantasy world in order to become who he really is.