In act III, scene 6, Lear—with his new, exiled "court" consisting of his Fool, Edgar, and Kent—stages a mock trial of his treacherous daughters, Goneril and Regan. On one level, the scene shows, as Kent says of Lear, that "His wits are gone." Yet it functions as far more than an illustration of Lear's madness.
While there is humor in referring to the Fool as "sapient" or wise, this "upside down" trial continues to reinforce the Fool's role as a clear-sighted and practical advisor. From the moment Lear gives away his kingdom in act I, the Fool tells him he is the biggest fool of all. Now the Fool continues as a truth teller, informing everyone that Lear's Goneril is a "joint-stool." This both indicates that Lear is addressing a stool and is an accurate insult aimed at Goneril, suggesting she is crude and not refined.
The scene also helps raise our sorrow and pity for Lear, who was once a mighty king and is now reduced, as a child might be, to play-acting a trial that relieves some of his anger at how he has been mistreated. He is a royal, even if deposed, and we are not meant to treat him as a joke, as we might a "rustic." As Edgar says in aside, prompting how we are supposed to feel:
My tears begin to take his part so much,
They’ll mar my counterfeiting.
Further, as Edgar also states, sharing one's grief and pain is therapeutic. It helps Edgar to hear Lear's sadness and know he, Edgar, is not alone in having been betrayed by a heartless family member, and it helps Lear (who at the end of the scene is able to fall asleep) to enact his suffering around sympathetic friends. Edgar says: "Who alone suffers, suffers most i' th' mind." He then points out that friends make any sorrow easier to bear.
Finally, we see that while Lear has given up the power and outward trappings of monarchy, he still feels inside as if he is king. This is a key to his "madness:" to him, his authority is divinely derived, and his great shock is that other people, such as his daughters, see it crudely as only based on the land and money he once had, not as a quality integral to his being.