It is ironic that Ralph does not notice that his nails are bitten until he becomes aware of the hopelessness of his and the boys' situation: When they stop to eat some fruit--which is all they have been surviving upon--Ralph considers their griminess, wishing that he could bathe and wash his clothes. Glancing at his hands, he sees that his nails have been bitten to the quick. Probably, Ralph has bitten his nails out of nervousness or preoccupation with other thoughts.
Ralph ponders the remoteness of their being rescued. He considers whether they might be able to be saved if they move to the other side of the island. Tense, Ralph grips a rock, arches his back, and opens his mouth. At this point, he may feel the pressure of Jack's rivaling him for leadership. For, later in the chapter Jack mocks and challenges Ralph's leadership: "Bollucks to the rules! We hunt" he says. This rivalry, of which Ralph feels the strain, is Golding's portrayal of the struggle of brute force (Jack) against society's rule and order (Ralph).
In Chapter Seven of Lord of the Flies, Ralph discovers that his fingernails are bitten—a nervous habit that he has unconsciously picked up because of the stress he is under on the island. Ralph notices this while the boys stop to eat some fruit. It is clear that the boys' situation is more dire than the leaders of the group let on. Being in charge of these children has proved to be a herculean task, particularly with the divisive presence of Jack, who questions and challenges Ralph in a persistent way. With his leadership being constantly undermined, Ralph has to use every ounce of mental energy to keep the group together and safe from the chaos that Jack would otherwise instill. His bitten fingernails are a physical sign of the intensity of this situation.