He was born to Pasiphae, the wife of King Minos of Crete. To prevent the minotaur from eating his own people, Minos had the minotaur shut up in a complex labyrinth designed by Daedalus, who had also built the contraption that had permitted Pasiphae to be impregnated by the white bull of Poseidon.
[3.1.4] But angry at him for not sacrificing the bull, Poseidon made the animal savage, and contrived that Pasiphae should conceive a passion for it.18 In her love for the bull she found an accomplice in Daedalus, an architect, who had been banished from Athens for murder.19 He constructed a wooden cow on wheels, took it, hollowed it out in the inside, sewed it up in the hide of a cow which he had skinned, and set it in the meadow in which the bull used to graze. Then he introduced Pasiphae into it; and the bull came and coupled with it, as if it were a real cow. And she gave birth to Asterius, who was called the Minotaur. He had the face of a bull, but the rest of him was human; and Minos, in compliance with certain oracles, shut him up and guarded him in the Labyrinth. Now the Labyrinth which Daedalus constructed was a chamber “that with its tangled windings perplexed the outward way.”
Book 3 of the Library of Apollodorus, Tran. by J. G. Frazer
To keep the minotaur fed, Minos ordered the Athenians to send over 7 young men and 7 young women each year. When Theseus heard the wails of the families on the day on which the young people were to be sent as feed, he volunteered to replace one of the young men. He then went to Crete where, with the help of one of the king's daughters, Ariadne, he was able to solve the labyrinthine maze and slay the minotaur.
[See #9 on Thursday's -cide words to learn.]