The most important thing that we learn about Jim in these chapters is that he is extremely unselfish. We find that he truly loves Huck and Tom and that he is willing to put his own desires aside in order to help them.
We see this best in how Jim acts after Tom is wounded. Tom's wound has been incurred as he carries out his silly plan to "help" Jim escape (Jim could easily have run off whenever he wanted and Tom's plan only makes it harder). Jim could well be expected to just try to escape since freedom has been his major goal. But he does not -- he stays to help Tom even though Tom has been making his life difficult with his plan.
This shows how very selfless Jim is.