According to Hesiod, Calypso is one of the many Oceanids.
In the Odyssey, Odysseus eventually washed ashore on the island of Ogygia, which was ruled by Calypso. She and her maidens nursed Odysseus back to health. The two became lovers. She offered him an immortal life, but he refused, preferring to once again return to Ithaca and see his wife and son. Odysseus lingered on Ogygia, spending his days staring at the sea and his nights in Calypso's bed.
Athena, however, was still looking after the king of Ithaca, just as she had done during the war. While Poseidon was away, she went to Zeus and asked him to aid Odysseus. He agreed, and sent Hermes to speak to Calypso, while Athena was sent down to Ithaca to aid Telemachus.
Hermes ordered to Calypso to allow Odysseus to return. She could not afford to defy the will of Zeus. She gave Odysseus the materials to build a boat, as well as the provisions to stock it.