What does the snake symbolize?
I think that you are asking about the "beast" that some of the littluns fear. Some of them fear that it is a snake, not a "monster" like you might imagine. They think it is a snake because they see "creepers," or vines, in the jungle at night and their imaginations take over and they are scared.
Their fear introduces the idea of evil to the island. If you look at snake symbolism, it goes back to the garden of Eden story in the biblical book of Genesis. In that story, evil enters the garden when a serpent, which is twined in the branches of the tree of knowledge of good and evil, tempts Eve into eating the fruit. She then gets Adam to eat from this forbidden tree as well and the two of them are subsequently exiled from the garden because they disobeyed God. Golding's use of the snake in Lord of the Flies introduces evil (through fear) into the island society. Once that happens, the society soon breaks down, the boys become more and more uncivilized, and murders occur.
More than anything else, it symbolizes fear. Specifically it represents fear of the unknown. Jack uses the littleuns' fear of the snake, the mythical "beastie," to consolidate his own grip on power. He knows that the "beastie" doesn't actually exist, but so long as the younger boys believe that it does, they will look to him as their protector. It's far better for Jack if the other boys' fear is diverted to something non-existent than to what should be an object of genuine fear—namely Jack himself.
It's also possible to interpret the snake as a religious allegory. Just as the snake tempted Adam and Eve to eat from the tree of knowledge, so Jack tempts the littleuns into believing that there really is a hideous, snake-like creature lurking behind every tree and bush. When Adam and Eve first listened to Satan, the result was sin and death; when the boys come under the sway of Jack's demonic power, the deadly consequences are much the same.