It may seem like a small and seemingly non important object, but it represents that cole now no longer wishes to hurt Peter, he wants to help him heal and he wants them to become friends.
"I'm not going to hurt you, I just brought you this." (P218)
It represents Cole's ancestors up until the moment he pushes the rock down the summit, at that moment he lets go of his ancestors and turns the rock into his anger.
"Pretend the rock is your ancestors, you take them with you but leave your anger" (P155)