Why does Pip want to go back home? What does he find when he visits Satis House?
I assume you are talking about the end of the book. Pip wants to go home and talk to Joe. He wants to ask him for forgiveness for how he's treated him. He also wants to repay Joe for all of his bills. He's finally matured and realizes how he's treated Joe since he's come into his "great expectations." While he's home, he wants to propose to Biddy. She's the one who was always good, always pure, and he should have seen it long ago. Those are the reasons he wants to return home.
Then in the last chapter he returns to Satis House and finds Estella there. He finds that she has been all but broken by Drummle. But he had an accident and died. She and Pip decide to never part again (in the second ending--the one I like better).