In Book 6 of Homer's Odyssey, Odysseus has been shipwrecked and manages to swim ashore on Phaeacia. When he comes ashore, he has lost all of his clothing. When he encounters Nausicaa and her maidservants, he does not want to bathe in front of them because, as he says, "I am ashamed to stand naked among lovely women" (A.S. Kline translation). Thus, on the surface, this shows Odysseus as a modest person. There is more to it than this, though.
Bathing occurs in numerous places in Homer's Odyssey and, in several places in the epic, men are bathed by women. I have not checked all these instances of women bathing men, but I suspect that one of the distinctions made by the Greeks would have been one of slave woman versus free woman, as well as freeborn married woman versus freeborn unmarried woman.
It was probably socially acceptable for a Greek male to be bathed and/or seen naked by a slave woman, but it was not socially acceptable for a freeborn woman to see naked a man who was not her husband. Because Nausicaa is both freeborn and unmarried, it is probably not socially acceptable for Odysseus to appear naked before her. Thus, Odysseus' refusal to bathe before the women, in particular, Nausicaa, shows his respect for the social custom.
Earlier in Book 6, Nausicaa is compared to Artemis, a virgin goddess. This comparison highlights Nausicaa's unmarried status. If Odysseus had appeared naked before the real Artemis, the goddess probably would have destroyed him.