When would someone need surgery on their teeth?

Fillings! Simple dental fillings, root canals and extractions are all examples of "surgery on a tooth" fixing cavities is a surgical procedure!
What type of sx ? Extractions, periodontal surgery? You did not say. But extractions are performed when teeth are no longer restorable or treatable, and periodontal surgery is performed when the support mechanisms of the teeth have become compromised.