Nymphs are divine spirits who represent certain natural forms. They often occupy a "liminal" space--meaning a space "in between." They are in between human and god, in between nature and civilization, in between terrestrial and maritime. This is a good representation of the entire epic, because the Odyssey itself is a kind of liminal work. It too, falls in between a lot of things (including in between the land and the sea).
Also, far more concretely, Calypso is a nymph. She represents the largest chunk of Odysseus' time in between the Trojan War and his return home. She keeps him hostage on her island of Ogygia for seven years, hoping to keep him as her husband. He grows more and more dejected during this time. Even though she treats him well, and they eventually sleep together, he become more reflective of his endgoal. He desperately wants to get home to his wife and son, even though Calypso continually offers him immortality and a life of happiness.
Athena, Odysseus' guardian goddess, sees his wretched state as Calypso's captive, and begs her father Zeus to let him go. Zeus sends the messenger god Hermes to tell Calypso to release Odysseus. Although Calypso is angry and heartbroken, she realizes that she must let him go because of his unhappiness. She gives him provisions and let him leave on a small raft.
Isn't Calypso a nymph? I think that the nymphs serve the purpose of a foil to Odysseus and brings out the qualities of what it is to be human and to long for something, in this case home. To stay with Calypso for so long, shows his more human side and qualities that a person can do something like that with a wife at home if he has no alternative but to persuade someone to let him go.