There are a couple points that are significant about the boy finding his own drawings in the chest.
The chest was long the repository of things important to his mother. Finding his drawings in there showed him how his mother felt about him. He had created something that his mother deemed so important that she could not throw away.
The chest was also the repository of old things, things from the past. By finding his drawings in there, it was proof that his childhood was over, a thing from the past.
