One significance of this story is the way it reflects on Jim and his humility. The story, importantly, demonstrates that Jim's humility is not borne out of his "social condition" as a slave, but instead stems from his experience with his family.
Lizabeth, Jim's deaf daughter, taught Jim a potent lesson about assumptions, compassion, and empathy. He had thought his daughter was not minding his instructions and he went so far as to strike the young girl. Then he discovered that she could not hear his instructions. She was deaf.
Jim is naturally saddened and humbled by this experience. In his willingness to recount the story to Huck, Jim demonstrates that this humility is now fully incorporated into his character. This humility contrasts with Huck's continuing juvenile tricks and slight abuses of Jim and Jim's patience.