An air-breather was anyone who inhaled gaseous air rather than water. It was a term used to describe those that remained to live on the "surface places" of planet Argo. According to Ruling Tribunal of the Aquans, the ancient Aquan records said that air-breathers were the enemies from the surface, who never came in peace, and whom the Aquans expected spies from for a long time.
In 2269, Cadmar referred to James T. Kirk and Spock as air-breathers, telling them to leave. When told they were surface dwellers from another planet, Cadmar dismissed their lies, fearing they were there to destroy the Aquans. (TAS: "The Ambergris Element")