His fainting may show a physical weakness in Simon's character. His body isn't capable of doing "x" and it shuts itself down completely. Or maybe it's a sign that something is actually physically wrong with him.
I think it more importantly is tied to his importance as an emotional character in the novel. Simon is a calming influence on many of the boys, especially the Littluns. He's not quick to jump to crazy conclusions about monsters in the jungle, and even suggests that they are all really only afraid of themselves.
When Simon goes to his peaceful place and finds the head of the pig on the stick, he imagines having a conversation with the Lord of the Flies. Simon learns that he was right all along. The monster is the boys themselves. It is their own individual capabilities of doing great harm and evil to each other. He learns that each person is capable of releasing an inner darkness.
I think Simon faints because he can't handle the thought that he is capable of such atrocities. Or he faints because he realizes that evil IS indeed within him, and Simon faints as a way to stop the conversation and keep that evil at bay. In that last way, his fainting signifies Simon's physical refusal to hear any more of what the Lord of the Flies has to say.