This scene opens with an iconic image: Lear, a white-haired man, stands on a heath in the middle of a thunderstorm yelling at the sky. "Blow winds and crack your cheeks! Rage, blow!"
The Fool begs Lear to go back to his daughters for shelter, but the King refuses; he would rather face the relentless elements than his ungrateful children. He never gave the weather his kingdom, so he can't fault nature for mistreating him. His kids on the other hand...
Kent shows up, still disguised, and tells Lear he has to find shelter.
Lear keeps yelling into to the wind. He calls for the storm to reveal all the crimes people have committed, kind of like the way strong winds strip away tree limbs and soil. He wants the storm to uncover everyone who's been unvirtuous, and he says if that happens it will be clear that he's been more of a victim here than a perpetrator. (He says: "I am a man more sinned against than sinning.")
Finally, Kent manages to maneuver him towards a hovel that will provide some shelter against the rain. He says that while Lear rests in the hovel, he'll go back and demand shelter from Lear's daughters again—even though they're so hard-headed they wouldn't even answer the door last time he knocked.
"My wits begin to turn," Lear mutters. But he has enough clarity of mind left to comfort his shivering Fool. Lear says, "Poor fool and knave, I have one part in my heart that's sorry yet for thee."
The Fool sings a little ditty (which sounds a whole lot like the song Feste sings at the end of Shakespeare's play Twelfth Night, btw) and Lear and Kent seek shelter.
The Fool delivers a witty speech predicting that Britain will "come to great confusion" when priests are corrupt, beer-makers water down their beverages, when pickpockets stop preying on large crowds, and when "bawds and whores" build churches. In other words, these things happen all the time so, Britain has already fallen into decay. Get it?
The Fool also predicts that, in the future, Merlin (the legendary wizard in King Arthur's court), will make this very same prophecy. (Note: Lear is set in ancient, pre-Christian Britain, long before King Arthur's reign in the sixth century, so Shakespeare's making a little joke about time here.)
Brain Snack: The Fool's "prophesy" is a parody (spoof) of "Merlin's Prophesy," a poem that was falsely attributed to Geoffrey Chaucer in George Puttenham's famous book called The Arte of English Poesie (1589). In other words, Shakespeare's giving a literary shout-out here.