What does the old spelling bee medal symbolize in To Kill a Mockingbird?

The spelling bee medal is one of the items that Scout and Jem find in the knothole of the tree, which the reader assumes were left by Boo Radley. Collectively, these objects are Boo's way of interacting with the children, though his motives are unclear. One possible explanation is that he wants to contribute to their childhood fantasy by growing the mystery.

Each item that Boo leaves, with the exception of the pennies, is of no monetary value, but to a child they could be priceless. Things like twine, pennies, and a broken watch are what we might consider garbage, but to Scout and Jem they fuel the excitement and fantasy world that occupies their free time. The soap dolls and spelling bee medal, on the other hand, are much more personal items and their presence in the knothole gives the occurrences more complexity. The hand-carved soap dolls, one could assume, are a symbol of affection or appreciation, as they are carved to look like Scout and Jem. The medal, has more to do with Boo than the children.

Throughout much of the book, the children view Boo (who they've never actually seen) as a kind of mythical monster. He is a source of fear and excitement that is fueled by town gossip and urban legend. In light of that, leaving the medal in the knothole is Boo's way of communicating to Jem and Scout that he was once a normal child, just like them.