In my opinion, this kid represents sort of the bad side of human nature or the bad side of the narrator of the story.
In the story, the kid comes along after the hanging and seems totally oblivious to what just happened. He does not care at all about the dead man. In fact, he is laughing at him for having been so scared when his appeal was denied. Instead of caring about the man, he cares more about his new cigarette case.
So I think he represents the side of human nature that is selfish. This is the side that does not care about other people and their problems. It is the side opposed to the one the narrator is showing (the side that thinks what happened was terrible).