Bettas are anabantids (of the Family Anabantidae), being fishs with an auxiliary breathing apparatus known as the labyrinth organ, that enables them to respire by breathing directly from the surface of the water. Taking air into their mouths and passing it over the labyrinth organ and out of their gill slits supplements the more usual breathing by way of gills. Other fishes with labyrinth organs include the other Betta species and gouramies.
The origin of the scientific name, Anabantidae, derives from the Greek verb, anabaino, meaning "to ascend" or "to go up", referring to the habit of such fishes as they swimming to the surface to respire.
Having two methods of breathing increases the survival opportunities for Bettas. It is this organ that enables us to keep Bettas in small containers.
The labyrinth organ enables Bettas to live in oxygen depleted waters, under conditions that would be lethal to most other fishes. The warm waters in which Bettas live are often poor in available oxygen.
The labyrinth organ is a wonderful adaptation for survival that enables Bettas to extend their habitats into rice paddies and ditches.
source : http://watershed3.tripod.com/anatomy.html
