Lord of the Flies
The beast is easy enough: it represents evil and darkness. But does it represent internal darkness, the evil in all of our hearts, even golden boys like Ralph? Or does it represent an external savagery that civilization can save us from?
Now You See It
At first, the beast is nothing more than a product of the boys' imaginations. The smaller boys are afraid of things they see at night; rather than be blindly afraid of The Great Unknown, they give their fear a name and a shape in their minds. You can't defeat a "nothing," but you can hunt and kill a "something." (It's kind of like how Voldemort was a lot scarier before we saw him as Ralph Fiennes.)
And then an actual "something" does show up: the dead parachuting man, who seems to come in response to Ralph's request for a "sign" from the adult world. It's ironic that the best the adults can come up with is a man dead of their own violence: maybe the beast isn't just confined to the island.
Now You Don't
And now we start getting some real insight into the beast. Piggy basically says the beast is just fear of the unknown: "I know there isn't no beast—not with claws and all that, I mean—but I know there isn't no fear, either" (5.99). Simon, on the other hand, insists that the beast is "only us" (5.195). Well, it is: it's a person that fell from the sky. When the twins list off the horrible attributes of the creature they saw, they reveal that it has both "teeth" and "eyes"; Ralph and Jack see it as a giant ape. So the "beast" is a man-who-isn't, the animal side in all of us.
But even that isn't quite what Simon means. He's talking about the beast being the darkness that is inside each and every one of us. If this is true, then, as the Lord of the Flies later suggests, it is absurd to think that the beast is something "you could hunt or kill" (8.337). If it's inside all of us, not only can't we hunt it, but we can never see it, never give it form, and never defeat it.