There are two overarching conflicts in Lord of the Flies. The boys stuggle to survive on the island, which is a life and death conflict. This conflict serves as the background for the book's drama and for its other large-scale conflict relating to the question of civility.
Though the boys do have fruit and fresh water as well as fire on the island, so ensuring survival is not especially difficult. Yet a young boy dies early on when the group attempts to make fire for the first time and the fire gets out of hand, burning a whole section of the island.
Death is a real possibility and the boys are certainly, actually stranded. This means that survival (life vs. death) ranks as one of the central conflicts of the novel.
Civility, however, is the critical dramatic conflict of Lord of the Flies. Can the boys maintain their humanity in the face of difficulty? Can they create rules and follow those rules, work together, and form a functional society?
These questions are at the heart of many of the moments of conflict which emerge in the story. Jack and Ralph differ on exactly these issues, with one boy representing disorder and inhumanity and the other representing a will to follow rules and keep order.
Ralph tries to maintain order and convince the boys to work for the common good, but he can't overcome the selfishness of Jack and his hunters.
The climax of the novel depicts the victory of incivility in this central conflict as Ralph flees for his life from the group of young savages that intend to kill him. Animalism wins and humanity loses in the microcosm of the society of the island.