It can be argued that there are several themes in Lord of the Flies, and it's difficult to say which of them is the most central to the text. We might also distinguish between what the text explicitly says, and what is implicit (these are the thematic concepts and thematic statements); this is important because the many books are not necessarily forthcoming about what their theme is supposed to be. In the Enotes link below are details on several themes that are commonly identified in Lord of the Flies, such as Good vs. Evil and Reason vs. Emotion. However, I think the central theme is closely linked to the narrative conflict of Man vs. Self: Civilization is a thin veneer that struggles to contain the beast within us.
As you might assume, I think that the Beast is probably the most important element in understanding the theme. We could almost think of the Beast and Simon as the true narrators of the theme, will all of the action taking place in the "background", progressing towards what seems to be an inevitable conclusion. The Beast even seems to gain power, going from being an unidentifiable "thing", to becoming embodied in the paratrooper, and finally speaking and giving itself titles (the Lord of the Flies) in the form of the pig's head.
The connection between the Beast and humanity is made early in the story, and only grows over time;
However Simon thought of the beast, there rose before his inward sight the picture of a human at once heroic and sick.
Simon, possessing an abstract and visionary sense, figures things out even if he's not really aware of the meaning.
There isn’t anyone to help you. Only me. And I’m the Beast. . . . Fancy thinking the Beast was something you could hunt and kill! . . . You knew, didn’t you? I’m part of you.
The Beast itself makes things pretty clear.
I think we could tell the story of Lord of the Flies, at least in terms of its themes, with only the characters of Simon and the Beast. The other boys and the action that takes place on the island is almost like a separate story; this is also emphasized by Simon's isolation and choice not to interact with them. In essence, we see the theme "acted out" by the boys, whereas Simon acts like a one-man Greek chorus, telling us more pointedly what that theme is.
In terms of how this is evidenced by the boys, we can clearly see many symbols of power, both civilized and savage, that the boys use as they transition from an orderly society to a wild one. Much is made of the conch, and how it represents the rule of law, but equally important are the face paint, fire, violence and blood-drunkenness that the hunters come to be associated with. Psychologically these elements might be considered to be part of a "collective memory", or instinct, buried within the human past, and emerging in times of chaos to reveal who we "really are" without the restraints of civilization to keep us in check.
Individualism vs. Community
The main theme within Lord of the Flies is the ideas of being an individual or acclimating to the group. This idea is shown through the many situations the characters go through in each instant. Many of the situations lead the reader to believe that self preservation is more rewarding than honestly between the crowd. All characters gain the self fulfillment rather than want to better the community as a whole. This ultimately brings more issues to the island, which later adds to the conflict and resolution. The idea of individuality vs. community starts with one self desires.