The Minotaur is another one of those monsters that started out as a single creature in mythology and then became an entire race of creatures. This is similar to the Pegasus and Gorgon, who each began as a specific character in myth and eventually became the "brand name" of their race.

The original Minotaur of Greek mythology actually had a name - Asterius. He was the love-child of Pasiphae, who was the Queen of Crete, and a bull. Which explains why he had the head of a bull and the body of a man. (In most descriptions of later minotaurs, they also have the legs and tail of a bull, as well as the head, but the original Minotaur seemed to just have the head of a bull.) 

Pasiphae gave birth to Asterius, the world's first minotaur. A guy named Minos freaked out and made Daedalus, the famed architect/engineer of the kingdom, build a giant maze called The Labyrinth. He then forced his new stepson, the minotaur, to live in the Labyrinth forever, sending seven young men and seven young women each year into the maze to end up as food for the minotaur. Eventually the original Minotaur's days came to an end when one of the seven youths, Theseus, eventually got to the end of the maze and killed the minotaur.