In Act 3, Lear rushes from a fight with his daughters into a raging thunderstorm. It's going to be no surprise to you to hear that the combination of thunder and lightning is pretty much what's going on inside Lear's mind, from his fury at his daughters to his impending madness. At one point, Lear admits there's a "tempest in [his] mind" that's not unlike the storm that rages on the heath (3.4.4.). In other words, the literal storm on the heath is a pretty accurate reflection of Lear's psychological state. (If you've seen Lear performed on stage, you know just how dramatic and compelling the sounds of thunder and lightening can be as Lear rages against his wicked daughters.)
We can also argue that the storm parallels Britain's fall into political chaos. Remember, Lear has divided his kingdom, civil war is brewing, and the King (Lear) is being treated pretty shabbily by his daughters and some of his other subjects. (Psst. As it turns out, Shakespeare happens to be pretty fond of this kind of symbolism. In Macbeth, for example, storms are associated with the rebellion against King Duncan and the political state of turmoil in Scotland.)
Alternatively, we could say that the powerful storm in which Lear gets caught up is a dramatic demonstration of the fact that all humans, even kings, are completely vulnerable to overpowering forces like nature. If you like this idea, check out our discussion of "Nakedness" below.