It's just an innate skill that increases the amount of damage that your punches do if you auto attack with no weapons equipped.
I'll bet the people who participated in this competition would have something to say about it: https://www.shroudoftheavatar.com/f...s-get-your-fight-on-in-stormsong-vale.146172/ @MelfromHell
People asked for unarmed combat for a very long time, so once upon a telethon (when they were still called telethons), Chris set an impromptu stretch goal that he would add pugilism if we hit a certain dollar amount. He never promised it would be good, and it's still kind of a silly/joke skill. Who knows, maybe one day it will actually be a thing, but as others have said, I doubt it will be any time soon.