William Golding said he wrote Lord of the Flies in "an attempt to trace the defects of society back to the defects of human nature." If that is so, then one of the primary themes in the novel must be that when mankind has no restraints (such as the authority of law, the norms of society, or his own conscience), he will devolve into savagery.
We see ample evidence of this theme in many characters, but it is particularly evident in Jack. It is Jack who spends his days hunting and who eventually begins painting his face so the pigs will not notice him. When he does, a drastic transformation (which is not just physical) takes place, Jack looks at his reflection in the water.
He looked in astonishment, no longer at himself but at an awesome stranger. He spilt the water and leapt to his feet, laughing excitedly. Beside the pool his sinewy body held up a mask that drew their eyes and appalled them. He began to dance and his laughter became a bloodthirsty snarling. He capered toward Bill, and the mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness.
Without shame and his conscience to maintain his morality, Jack becomes a savage. This innate savagery in the unrestrained man is one theme in the novel.
Other themes, as mentioned by the previous answer, include civilization versus savagery and a loss of innocence. Both of these themes are evident throughout the novel, but they are most obvious in the final chapters.
After Jack steals Piggy's glasses, Piggy can take no more and is ready to instigate a final confrontation between himself and Jack. He carries the conch, symbol of order and civility, and he shouts this question at Jack:
“Which is better—to have rules and agree, or to hunt and kill?”
The answer comes in the form of a boulder which crushes both Piggy and the conch. All civilized behavior is gone and savagery is all that remains.
When the naval commander arrives, Ralph's life is spared and he can finally become a boy again, as he was at the beginning of the novel.
[W]ith ﬁlthy body, matted hair, and unwiped nose, Ralph wept for the end of innocence, the darkness of man’s heart, and the fall through the air of the true, wise friend called Piggy.
Unfortunately, he is not the same boy because he has lost his innocence, as have all the others on the island.
These are three of the significant themes found in this novel: man is innately savage, civility versus savagery, and loss of innocence.