When Jim tells Huck about his family, and in particular his deaf daughter, Huck realizes that Jim's feelings run deep. The equality of humanity shared between Huck and Jim becomes clear to Huck.
We learn that Jim is a normal, natural human being with feelings and fears from his discussion of his deaf daughter. More pointedly, we learn that Jim possesses great humility that has been learned. This humility is not borne out of his social position, but out of his experiences with his family.
This humanity in Jim is not a surprise to most readers, however, it is a surprise to Huck. We learn as much about Huck Finn from his reaction to Jim's story as we do about Jim.
Huck comments that Jim felt about his wife just as deeply as any white person would feel. The notion that this would be a revelation to Huck suggests his naivety and his profound and blind agreement with the perspectives of his culture up to this point.