An aquarium is a tank filled with water designed to hold species of life which require an aquatic environment.
Kirk and Spock were held in an aquarium in sickbay after a forced mutation restructured their lungs to work under water. Kirk remarked that he couldn't command the ship from inside of it. (TAS: "The Ambergris Element")
A Halo fish was kept as a lab animal in a small aquarium in sickbay of the USS Enterprise. (TAS: "The Terratin Incident")
A makeshift aquarium was created on a captured Klingon Bird-of-Prey to transport George and Gracie to the 23rd century. (Star Trek IV: The Voyage Home)
Captain Jean-Luc Picard kept a fish named Livingston in a spherical aquarium in his ready room. (TNG: "Encounter at Farpoint", "We'll Always Have Paris")
Wesley Crusher had an aquarium in his quarters in 2365. (TNG: "The Dauphin")
An aquarium was part of Doctor Paul Stubbs guest quarters aboard the USS Enterprise-D. (TNG: "Evolution")
In early 2366, Counselor Deanna Troi kept a small aquarium in her quarters. (TNG: "The Survivors")