What does the death of Simon in "Lord of the Flies" signify?specify the relation between this death and the threatening of the piglets head, that...

Simon's death is the beginning of the end in the novel.  It signifies the end of civilization,  and goodness.  It is as if "good" is being destroyed.

He actually dies as he is trying to explain the "beast" to the other boys. He never had the opportunity to explain that the beast was within all of them. The boys continued to become more and more savage until this point.  They do not realize how bad they have become until Simon is killed in their chaos.