A leviathan is defined as an extremely large sea creature or monster, such as a blue whale. There have been many reports, throughout history, noting sightings of enormous sea-dwellers which displayed devastating power and destructive force, sometimes leading to the destruction of ships and even entire fleets. Most of these are, however, the stuff of legend and myth. Reference to a leviathan metaphorically refers to something huge, threatening and dangerous.
In this chapter, Sam and Eric had just seen what they believed was the beast and had rushed to inform the others. The boys, except Piggy and the littluns, set out to find it. At a certain point, Ralph and Jack continued the search alone and Golding describes Ralph's perception as he looks over the ocean:
Now he saw the landsman’s view of the swell and it seemed like the breathing of some stupendous creature...
...Then the sleeping leviathan breathed out, the waters rose, the weed streamed, and the water boiled over the table rock with a roar. There was no sense of the passage of waves; only this minute-long fall and rise and fall.
The description implies a massive sea creature, asleep underneath the water, breathing in and out. It is as if when it breathes out, the water rises and recedes when it does the opposite. The rhythmic rise and swell of the water copies a breathing pattern. Obviously, there is no large sea creature and the image creates the impression that it is the ocean itself that is breathing.
Metaphorically, these actions represent the ebb and flow of the boys' lives on the island. There is continuous movement signified by periods of peace and tranquility, when the boys work together, and conflict, when they oppose one another - more particularly illustrated by the behaviour of Jack and his hunters on the one hand, with that of Ralph and the other boys on the other.
Symbolically, the sleeping giant suggests an enormous threat. When it awakens, great harm will ensue. Underlying the boys' existence and their survival, is the threat of their innate savagery which will expose itself later. No one will be spared. Even the more civilized boys, such as Ralph and Piggy will reveal their instinctual bestiality such as when Ralph is overwhelmed by the lust to hurt and participates in the hunting game, when he relishes the fact that he had hurt a pig and later, when he and Piggy, albeit unknowingly, participate in Simon's murder.
On a greater level, the 'sleeping leviathan' alludes to Man's irrational and natural desire to destroy and, in the process, becoming self-destructive. It is this flawed aspect of humankind's character that is the greatest threat to its survival. Awakening it will, surely, ultimately result in its annihilation.
Physically speaking, the "sleeping leviathan" is the giant of the ocean. The tide works in such a way that, in this particular spot near the castle rock, the water is sucked down over the course of a minute around this flat table rock and then it erupts again at the end of the minute and rages around and over the rock with incredible violence.
But the ocean in this case also likely symbolizes the sort of sleeping violence that is just beginning to show with the discussion and fear of the beast and the way that Jack and Ralph are beginning to fight more openly for control. The urge to hunt and kill and to throw off the trappings of civilization is powerful and surging forth after the moments of calm, just as the ocean seems to be quiet and receding for a minute only to return with such violence.
The raging influx of the tide also serves to highlight the isolation of the island itself and the fact that a rescue is not likely. This isolation only serves to exacerbate the trend towards mania that the boys seem to be demonstrating at this point in the novel.