Pegasus is the name of an immortal winged horse in Ancient Greek mythology. He was born from Poseidon and the blood of the decapitated medusa. As such, he was capable of creating springs, such as Hippocrene. Pegasus would be captured and tamed by the hero, Bellerophon, and would be used in many battles, including against the Chimera. Bellerophon would attempt to fly to Mount Olympus using Pegasus but Zeus, angered by this act, sent a gadfly to sting pegasus. It did and caused Pegasus to kick Bellerophon off his back, who ended up dying. Pegasus would be taken in by Zeus and would be his carrier of his thunderbolts. (other more rarer stories depicted that Zeus killed Pegasus, along with Bellerophon. The former tale was much more common than the latter tale). Pegasus would eventually be awarded for his service by becoming the constellation under his name.
Pegasus or Pegasi (Plural) can be used as a way to describe the species of winged horse, however, it is technically incorrect if you consider the fact that ancient greek word, Pterippus was the word that described that. Despite being incorrect, it is still generally accepted in modern times anyway.