The Fool, ironically, is a wise voice in King Lear. He makes satiric but seriously observant remarks. The Fool serves a role similar to that of a chorus. In Greek plays, a chorus was a group of people who comment on what's going on in the play, similar to a narrator. The function of a chorus was to give supplementary and background information. Lear's Fool functions more as a voice of reason for Lear.
Evidently, the Fool is quite loyal to the king. He uses humor to help him get through his sadness and reason to combat his increasing madness. The Fool is able (allowed) to be honest with Lear because he has a license to do so. To be unlimited enough to be funny, Lear allowed the Fool to say whatever he wanted. Combined with this license, the Fool's loyalty to Lear, and his objectivity, the Fool makes accurate, honest statements about what he sees. The Fool acts as part of Lear's conscience, still like a satiric voice of reason when Lear has a bout of madness.
Fittingly, when the Fool disappears at the end of Act III, Lear loses most of his reason and becomes quite mad (insane). As to why the Fool leaves in this scene is up to interpretation. One suggestion is that the Fool and Cordelia were played by the same actor; the Fool had to leave in this scene to allow the actor to change before her (Cordelia's) next scene.