Simon has the power of "seeing" and understanding what the other boys cannot. When the boys worry about the beastie, it is Simon who suggests that the beast might be within them, and it is he who has the encounter with the "lord of the flies," which is so powerful that it makes him faint. He is killed as the other boys celebrate after a hunt. Because his name is associated with Christianity (Simon Peter, Christ's chief disciple), we can understand his death as a sacrifice resulting from the pagan sacrifice of the pig.  See enotes character analysis of Simon and all the characters in Lord of the Rings by following the link below.

What is the purpose of Simon in Lord of the Flies?

Though Simon doesn't say very much for a good part of the novel, he has a very significant role that is essential to the development of the plot in Lord of the Flies.  Comparitively, and on a very basic level, Simon is the only one of the boys who is able to resist the savage behavior that inevitably overtakes the rest of the boys (even Ralph, at one point) on the island. 

More specifically, many critics see Simon as a Christ figure; he is one with nature, is inherently good, and dies trying to save the boys by reporting to them that there is no beast on the island.  Simon's encounter with the lord of the flies can be compared to Jesus's encounter with Satan. (One name for a demon in the Bible is Beelzebub, which, translated, means "lord of the flies"). 

Golding's description of Simon's death is vivid in its imagery:

The water rose farther and dressed Simon's coare hair with brightness.  The line of his cheek silvered and the turn of his shoulder became sculptured marble. The strange attendant creatures, with their fiery eyes and trailing vapors, busied themselves round his head. 

Here, the fireflies Golding describes seem to create a halo around Simon's head, and Golding further describes the peace and tranquility of the world (as represented through this scene) to stress the importance and beauty of Simon's character.  Ultimately, without Simon, the boys have no hope of being saved from themselves.