The Minotaur is half-man, half-bull. He was the son of queen Pasiphae of Crete with a white bull Poseidon sent from the sea. The white bull was supposed to have been immediately sacrificed to Posiedon, but Pasiphae's husband King Minos was greedy and kept the bull for himself. In revenge, Poseidon caused the queen to fall madly in love with the bull. The monstrous Minotaur is the result of their union.
The architect Daedalus built a huge maze to house the creature, and it was fed a yearly diet of seven youths and seven maidens from Athens. Theseus kills it, finding his way back with the help of golden yarn given to him by Ariadne, Pasiphae and Minos' daughter.
Theseus takes Ariadne away only to abandon her on an island. But it ends happily for the heartbroken princess, as she is rescued and married by the god Dionysus, ensuring her a long life filled with fine vintages.
It does not end well for the Minotaur, and I have always felt bad about that. It wasn't his fault that his parents made such bad decisions.
From Borges' "The Book of Imaginary Beings" tr. A. Hurley:
The idea of a house built expressly so that people will become lost in it may be stranger than the idea of a man with the head of a bull, yet the two ideas may reinforce one another. Indeed, the image of the Labyrinth and the image of the Minotaur seem to "go together": it is fitting that at the center of a monstrous house there should live a monstrous inhabitant. . . .
The worship of the bull and the double-headed axe (whose name was labrys and so might well have evolved into "labyrinth") was characteristic of pre-Hellenic religions, which held sacred festivals in their honor, known as Tauromachias. To judge from murals, human figures with heads of bulls figured in Cretan demonology. The Greek fable of the Minotaur is probably a late and somewhat uncouth version of very ancient myths -- the shadow of other, still more horrific, dreams.