The primary mention of the trophy is part of the initial stage directions in Arthur Miller's play Death of a Salesman. Its central location foreshadows in a way the importance of Biff's successes in Willy's life.
The main character of the play, Willy Loman, is a man who really embodies a myriad of behaviors and complex emotions that have existed in him as a result of a very dysfunctional childhood.
We know that Willy is very young when his father abandons the household to seek for riches in Alaska. This makes Willy very attached to his older brother, Ben. However, we also know that Ben basically abandons Willy as well, at first hoping to find his father, but then striking it rich in the jungle.
It is arguable that the abandonment of two male father figures has rendered Willy a very insecure man who, now, has to grow up on his own, develop his own identity, and comply with the social expectations bestowed upon men during his time: To become a husband, a provider, and a father.
This being said, Willy transfers his insecurities onto his two children, who happen to be also (like in his case when he was a child) two brothers: Happy and Biff. It seems that Willy's natural paternal love for his children has mixed, in a dysfunctional way, with the philosophy of life that Willy has created as a result of his experiences.
In Willy's world being well-liked, popular, and being "the wise guy" is what secures your social success. Hence, he raises his children to be epitomes of these expectations. Biff, who is naturally good at football seems to be everything Willy would have wanted to be, himself: Well-liked, good-looking, and quite successful at what he likes to do.
Hence, what we have here is a father living his own live vicariously through his son's. Biff becomes Willy's personal hero, whom he wishes to mold and perfect the best way possible. Contrastingly, Happy does not get the attention that Biff gets and often is relegated to a second place where he is basically forced to admire Biff.
Therefore, given the fact that Biff has come to embody Willy's ideals, dreams, and aspirations for success, it comes to no surprise that Biff's trophy is being enjoyed mostly by Willy. This trophy indicates that it is Willy, and not Biff, who has truly "succeeded" and it is Willy, and not Biff, who really feels deserving of it. It is one of those cases where the parent is so involved in his child's life that he loses perspective of who plays what role in the parent-child relationship.