Phaeton, himself, is one the biggest symbols in this story. Check it: he goes on this big journey seeking his father the sun, right? Then when he gets there, he becomes determined to become the sun itself by driving his Dad's gleaming chariot across the sky. Whoa, dude wants to be the sun itself? Those are some pretty monstrous ambitions.
Throughout the centuries, the story of Phaeton has been used as an example of what happens when people let their pride get the best of them. If you try to climb too high, you're bound to fall. However, you can also see a kind of tragic beauty in Phaeton's doomed quest. He may have failed and failed miserably, but at least he had the courage to dream big dreams. And where would humanity be if no one dared to dream as big? Puttering around in the jungle, playing Parcheesi with chimps all day long.