Pegasus was the famous winged horse who sprang from the blood that flowed from Medusa's neck when Perseus killed her: Medusa was pregnant by Poseidon at the time, so Pegasus had Poseidon as its father.
The popular origin of the name is pege, 'spring of water', and the origins of at least two springs in Greece were attributed to a stamp on the ground of the horse's hoof, the most famous being the Hippocrene or 'horse spring' (hippos, 'horse' and crem, 'well', 'spring') on Mount Helicon. Hesiod, in his Theogony, gives the other well-known 'spring' connection when he says that Pegasus was 'so named from the pegai, the springs of the Ocean' (i.e. Oceanus).
On the other hand the horse's name may be derived in some sense from pegnymi, 'to make firm', 'fix', 'build', this possibly referring to the construction of a ship, in view of the name of his 'father'. Philologists point out, however, that the -asos ending of the name (Pegasos) shows that the real origin is pre-Greek.