The fool makes a brief, but memorable, appearance during Hythloday's story of the Cardinal's dinner party, where he ends up rather badly insulting another guest, the friar. Wondering why in the world this poor guy is being referred to as a fool? Check out "Fools" under Symbols, Allegory, and Imagery to get the full story (hint: they're not as foolish as they sound).
Like most fools, this fool primarily functions as a way of revealing not his own foolishness, but actually the foolishness of everyone else; here, that would be the friar. As the fool makes fun of the friar, it becomes clear that the fool knows just as much Biblical stuff as the friar (who, um, should probably know more) and shows that this friar is a total hypocrite.
Brain snack: hypocrite! Another handy-dandy Greek word—not invented by More this time—that describes someone who says one thing and does another. You know, like a dentist who's always snacking on candy, or, uh, a friar who doesn't know the Bible that well...
In fact, the more the friar tries to defend himself, the more ridiculous he looks—that's the power of the fool. And the Cardinal calls the friar out on this:
"'Perhaps you mean well,' said the Cardinal, 'but I think you would act in a more holy, and certainly in a wiser way, if you didn't set your wit against a fool's wit and try to spar with a professional jester.'" (2.27)
Other than exposing the hypocrisy of some Catholic ministers (this was something More really hated), the fool is also an example of the very issue that More, Hythloday, and Giles have been debating: how can you influence figures of authority? Well, the fool is one possibility because he can use his joking tone to deliver devastating criticisms. Chew on that.