To literally shit using your brain instead of your (or another's) anus. Most often done by people who want to make up definitions to words that don't really exist in order to appear in an online "definitions" database.
Most people posting things to "The Urban Dictionary" are just taking huge brainshits.
Hey Cody! Earl, Jordan and me just posted a definition of "ba-donk-a-dank". Of course, "ba-donka-donk" was already done, but we just wanted to brainshit. Aren't we cool?!
Branchshitty is a poor teacher at Brentsville DistrictHigh School who hates every student who’s opinion differs from his own. He fails students regularly because he doesn’t agree with them.
Man, did you get Branshitty?
Branshitty failed me because I don’t agree with his opinions.