That the book is called Uncle Tom's Cabin rather than just Uncle Tom points to the symbolic significance of the cabin to the novel. As the novel opens, Uncle Tom lives in a cozy cabin on the Shelby estate with his wife and young children. In a sense, the cabin symbolizes the American dream—that is, the possibility of independence and stability.
However, Uncle Tom's cabin is not like the cabin a white person might have, because Tom cannot own it. His life with the Shelbys, which would be humble and ordinary by white standards, has a level of precariousness as a result of his enslavement. Tom's home is provisional, based on the whims of his owners. Because he is a slave, he can be sold, and when this occurs early on in the novel, Tom loses his cabin and all it represents. The cabin—the American dream—is not open to Tom, hardworking and deserving as he is, because he is a slave.
Uncle Tom's cabin is more than the literal cabin he leaves behind when he is sold south. Uncle Tom carries a moral home inside himself from which he can never be dislodged. This home is built on the foundation of faith. Tom realizes his body can be owned by others, but he never gives up ownership of his soul.