This is obviously a loaded question--one that can only be responded to in a detailed essay. (And I'm assuming that's what your assignment requires.) Here are some points to consider that might help you plan your response:
William Golding wrote this novel to examine human nature and how stressful situations affect people's actions. The primary conflict present in Lord of the Flies actually centers around the boys' struggles against themselves; this is evidenced by the fact that Simon, after his encounter with the lord of the flies, tries to report to the others that there is no beast--that the beast they're fighting against is actually within them.
Different characters respond to the stresses of life on the island differently. Ralph is the boy who longs for order, and he tries to establish (and enforce) rules. Jack, on the other hand, promotes savage behavior through his insistence that the children hunt regularly--even when it's clear the boys are hunting for sport rather than for food. Piggy is the voice of reason, but he is powerless without Ralph. Simon, the purest child on the island, is able to resist the temptation to resort to savage behavior when the others are not.
Eventually, chaos reigns on the island, and boys die as a result. Simon is killed because he is mistaken for the beast, and with him dies the information that could save the rest of the children on the island.
Obviously, there are many other conflicts in the novel, but they all stem from this main idea.
I hope this was helpful. Good luck with your essay!