Odysseus met Calypso on her lush island of Ogygia.
He was washed up on the shore of her island.
Hermes tells Calypso to let Odysseus go.
Calypso offers immortality to Odysseus
When first met Odysseus is staring out to see on Calypso's island dreaming of getting home to Ithaca.
Calypso
Calypso has the power of immorality over Odysseus.
Hermes is sent down to Calypso, telling her that the gods wish for her to release Odysseus. Therefore, it is Calypso who allows Odysseus to leave, not Odysseus who 'manages to say no.'
Calypso
Calypso and Odysseus become lovers. Calypso offers Odysseus immortality and eternal youth if he would stay with her. Calypso does not aid Odysseus' escape until told to do so, so he seemed trapped on her island without a ship.
Calypso wants Odysseus to stay with her on the island forever.
Calypso