I suppose you could say that running into Jim represents a rebirth for Huck because it is the transition point from one part of the story to the next. Before he meets Jim, he is a subject -- things are happening to him. Adults are making him do this and that and they are fighting over who "owns" him. After he meets Jim, he becomes more of an agent -- he is actually doing things on his own.
The conflict that results from their meeting is Huck's conflict over what to do with Jim. He knows that society says he should hand Jim back to his master. He most certainly should not help him run away. But in some way, Huck feels this would not be the right thing to do. So he has to decide between following his own conscience and doing what society says he should.