The Beast in The Lord of the Flies represents the boy's fear.
The adult-less island is unknown and the boys fear the unknown. Coming from England, they have no experiences with what they find on the island. In the fire light and in the dark, ordinary things take on new and mysterious forms.
As children, we fear the dark because it hides, in our childlike minds, all the monsters that disappear in the light of day.
Whether he recognises this or not, Jack gets the upper hand. He appeals to the boy's fears and uses this to control them.
Ralph and Piggy understand that the beast exists in their minds but are unable to get the others to understand.
The boys give into these fears, offering sacrifices to the "Beast". They believe that if they give the Beast sacrifices, that the Beast will not harm them. At first they sacrifice the head of the wild boar but eventually Simon and Piggy are sacrificed. Ralph would also be the next victim if Jack and his tribe have their way.
For each boy the Beast is different. It is whatever they fear the most.