The trichobezoar, or hairball, has no specific symbolic meaning. As one part of Jim's superstitious nature, Jim attributed various types of powers and functions to a variety of objects. Jim believed that the hairball could be used to answer questions and provide information that could be helpful to those asking it for help.
When Huck comes asking about Pap's plans, Jim obliges by asking the hairball for some prediction, which it provides after being paid for its effort. Because Jim believes in the hairball, and because Huck believes that Jim is hearing a message from it, the fortune is told.
He said it would tell my whole fortune if I wanted it to. I says, go on. So the hair-talked to Jim, and Jim told it to me. He says: 'Yo' ole father doan' know, yit, what he's a-gwyne to do. Sometimes he spec he'll go 'way, en den agin he spec he'll stay...
Of course, the fortune, as passed from the hairball to Jim to Huck, has no definite predictions of any sort anywhere within it. It is a whole series of contradictory possibilities with no firm conclusions or information provided.