The aquatic support apparatus was a device that provided oxygenated water for a water-breathing lifeform. It consisted of a helmet filled with water and a backpack that contained the mechanism to keep the water full of oxygen.
After being mutated by the Aquan surgo-op, James T. Kirk and Spock became water-breathers and had to be kept in an aquarium in sickbay. While en route to the surface of the ocean planet Argo to visit the Aquans, they wore an aquatic support apparatus so they could breath. Similarly, the Aquans wore an aquatic support apparatus while they visited the Enterprise. (TAS: "The Ambergris Element")