Momo is a winged-lemur, a once plentiful (and mischievous) specie that lived with the Air Nomads and was often kept as pets. However since the war, it's believed that most if not all of the Air Nomads and their animals (winged-lemur, flying bison, etc) have died out.
Aang found Momo when he, Katara, and Sokka visited the Southern Air Temple, and is now his pet. Momo's name comes from the fruit it took from Sokka at the end of the episode when it joins the group. (Momo is Japanese for Peach)
As a winged-lemur, Momo has enhanced hearing and smelling, and can sense danger (or food) from far away. Despite the desolate appearance of the Southern Air Temple, for Momo to have still been there gives hope to Aang that his people are still alive.