After he was blasted from a volcano, Percy Jackson, son of Poseidon, crashed in the shores of a paradisiac island: Ogygia. There, he was taken care of by a beautiful girl who we later learn was Calypso, the daughter of the Titan Atlas. Imprisoned in an island that only appears to lost travellers, Calypso was paying for siding with her father in the original Titan's War.
She took good care of Percy for the indefinite time he spent there: feeding, healing and entertaining him, as she had previously done with countless heroes.
After a while, she asked him to stay, but he declined the offer; he had to go back to Camp Half-Blood, to his friends, and especially, to Annabeth.
Calypso let him go, as she could only do so once she had already fallen in love with him (and all the others before him); this was also part of her curse.