A Pegasus is a winged pony. They are born in Cloudsdale and all go through flight training in the city in the clouds. While many Pegasi remain in Cloudsdale all of their lives, some live in Ponyville and other places across Equestria. Some notable Pegasi include: Rainbow Dash, Fluttershy, and Scootaloo.
Princess Celestia and Princess Luna are not necessarily considered to be Pegasi, even though they have wings. They also have horns and are capable of magic, a big distinction from the rest of the ponies. They are more of gods than any other class of pony.