Biff's idea of the American Dream is to own a ranch out west and farm. He doesn't want to follow his father's path of trying to be a great salesman and (supposedly) end up rolling in easy money.
To pursue his dream, Biff goes to ask his former employer, Mr. Oliver, for a loan. Both Happy and Willie have the idea that Biff was a star salesman for Mr. Oliver, an idea heavily promoted by Willy. However, Mr. Oliver doesn't even remember who Biff is. He was just another nameless employee. There is no way Mr. Oliver will give Biff a loan.
Biff gets so disgusted with constantly living in the fantasyland his father builds that he decides to give it up and face reality. He tries to tell Willy that he, Biff, is nothing but a failure, not the huge success story his father has always wanted him to be. Biff hopes to give up the idea of the grandiose American Dream to live a sane, modest life in which he can find some real fulfillment.
I'm not sure that Biff has an idea about the American Dream. It is clear that he has a dream for his life and it is the direct results of his life with Willy. Biff wants to get away from Willy's idea of the dream; he wants out of the office, out of selling --- he says he wants to work outdoors where a man belongs. But I don't know if this is a dream or his reaction to what he learned about the illusion that Willy lived in. It isn't so much a "dream" as the reaction to what he saw as a "nightmare."