A planet-based pressure dome
A pressure dome built on an asteroid
A biosphere is an artificially constructed, contained area built within a pressure or atmospheric dome providing a life-supported habitat for a station, starbase, or colony built in an environment not ordinarily hospitable to life. Unlike space stations, biospheres are generally built on bodies such as planets or asteroids, allowing their inhabitants to survive on the surface within them. (DS9: "By Inferno's Light", "In Purgatory's Shadow")
An early example of a planet-based biosphere was the Genome colony on Moab IV, a self-contained colony of Humans founded in the late 22nd century. In 2368, the colony was almost destroyed by a stellar core fragment, but, with assistance from the USS Enterprise-D, the biosphere was rebuilt to withstand the fragment. (TNG: "The Masterpiece Society")
In operation in the 2370s, the Dominion prison facility Internment Camp 371 - originally used to mine ultritium - was built within a biosphere, located on an asteroid in orbit of a gas giant. (DS9: "By Inferno's Light", "In Purgatory's Shadow")
At least one space station-based biosphere was operation as early as 2375, when Species 8472 built a biosphere recreating an approximation of San Francisco and its Starfleet facilities in the Delta Quadrant. Known as Terrasphere 8, the facility was created with the intent of better understanding Starfleet in order to undertake a more efficient invasion. When the crew of the USS Voyager learned of this plan, heated negotiations occured which lead to the end of invasion plans. Following the negotiations, the crew spent some time on the biosphere. (VOY: In the Flesh)