The battle between Dionysus and Pentheus is the main conflict in the myth, and it's also chock full of some pretty deep symbolism about the nature of human beings. Dionysus is all wild and crazy, right? He wants everybody in town to come party at one of his crazy Bacchanals and worship his wine-swilling ways. Pentheus on the other hand, wants everybody to chill out and obey the law.
So in a way, you could say that wild Dionysus represents the chaotic side of human beings, whereas level-headed Pentheus represents our more orderly side. There's no doubt everybody deals with this conflict in themselves. We've all got that part of us that just wants to let loose and maybe do crazy things, but we've also got that logical part of us that knows the wild side will get us in a ton of trouble if we let it get too out of control.