According to ancient sources, Pasiphae was the daughter of the Sun god Helios and Perseis (an Oceanid). This means that Pasiphae was also the sister of Circe (a notorious enchantress who charmed the hero Odysseus).
Pasiphae married Minos, the King of Crete. She bore several children to the king, including Androgeos, Ariadne, Deucalion, and Phaedra. However, the Queen of Crete also bore another, more monstrous child, and not to her husband. This incident forms basis for the story of the birth of the Minotaur.
The legend is that Pasiphae fell madly in love with a beautiful white bull. This bull was one of the prized possessions of Minos, and the king so admired the creature that he refused to offer the bull as a sacrifice to the god Poseidon (some versions of the story claim that Poseidon gave the bull to Minos so that the king would in turn give it to the sea god as a sacrifice). Poseidon, however, got his revenge.
The god of the sea cast a spell on Pasiphae, making the poor woman desire the bull. There was no way to overcome Poseidon's curse, except to allow Pasiphae to consummate the union. So the clever craftsman Daedalus was called in to create a cow made of wood into which Pasiphae could be placed. And this is how the Queen of Crete satisfied her lust for the white bull. From this coupling, a beastly offspring - the Minotaur - was born.
Who's Who in Classical Mythology