The Fool is Lear's own stand-up comedian, sure, but more interestingly, he's the only guy that Lear allows to criticize him. (Remember, when Kent lips off, Lear boots him out of the kingdom and when Lear doesn't like what Cordelia has to say, Lear disowns her altogether.)
As in many of Shakespeare's plays, the Fool is actually really smart—and the only person who tells it like it is. Compare Lear's Fool, for example, to Feste in Twelfth Night – neither one of them are afraid to call their misguided masters "foolish" and they both function as characters that provide a lot of social commentary.
At the same time, the Fool is more than just a funny and brutally honest guy; he's also super-loyal. Along with Kent/Caius, the Fool braves the elements (which at times consist of rain, thunder, and lightning) with his master.
But the Fool is also a big mystery: what happens to him? He disappears after Act 3, Scene 6, and nobody ever explains where he's gone. The only possible reference to the Fool after that is in the final scene, when King Lear says "And my poor fool is hanged" (5.3.369).
This could mean a couple of things: 1) Lear might be referring to Cordelia with a pet name, "fool," since Cordelia has just been hanged by Edmund's goons. 2) Lear could be literally talking about his Fool—perhaps the Fool was also hanged by Edmund's henchmen or, perhaps he hung himself out of despair. It's hard to say what really happens to the Fool. Some literary critics even speculate that the Fool and Cordelia were played by the same actor. They never appear onstage together, so some scholars hypothesized that the part was double cast, and that the Fool had to disappear when Cordelia came back into the play.