Doing something comedically means trying to get a laugh. You might describe the funniest person you know as being comedically gifted — or you could just say they're hilarious!
Comedically comes from comedy and its Greek root kōmōidia, "an amusing spectacle." Anything that's performed or presented in a deliberately amusing way is done comedically, with the intention of making people giggle and guffaw. You can tell a story comedically, perform Shakespeare comedically, and even write your English essay comedically (you just have to hope your teacher shares your sense of humor).