I don’t think it means brain jokes but I’m not sure what it means. I’d rather have examples instead of definitions.
Paddy applies for a job at the building site.
The foreman asks him “What’s the difference between a joist and a girder?”
Paddy replied “Joyce wrote Ulysses: Goethe wrote Faust.”
Just as an FYI, “cerebral” in the context you’re talking about just means that humor is a little bit intellectual, and requires some knowledge or higher than average education on the part of the person hearing it. Here’s an example of a cerebral joke:
The Philosopher Rene Descartes is on an airplane in first class. (Already funny, since Descartes died in the 17th century). The flight attendant asks him “Would you like a glass of champagne?”
He replies “Hmmm. No, I think not” and promptly disappears.
This is funny because Descartes’ most famous quote was “I think, therefore I am”, meaning that his existence was established by the fact that he could think. So on the airplane, when he says “No, I think not”, he ceases to exist. You need to know that in order for the joke to work, so it’s an example of cerebral humor.
It means intelligent humor. For example:
Question: What do you get when you cross the Godfather with a philosopher?
Answer: An offer you can’t understand.
Descartes is sitting in a bar, having a drink. The bartender asks him if he would like another. ‘I think not,’ he says and vanishes in a puff of logic.
And just for the record, I didn’t get half of those jokes. I just don’t know the facts they are based on.