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.
Related ThreadsGB's Guide to Pony Fanon! - last post by @ Aug 12, 2012
[My Weekly Pony] Ep. 5 - Griffon the Brush Off - last post by @ Dec 4, 2014
[My Weekly Pony] Ep. 2 - Elements of Harmony - last post by @ Dec 4, 2014
My Little Pony: Friendship is Magic - Fanfiction Contest! - RESULTS ON PAGE 7 - last post by Bread Effect @ Nov 10, 2011
Create Your Own Pony - last post @ Oct 13, 2014