A shower is an area where one bathes under a spray of water.
Showers were present on Earth Starfleet vessels during the mid-22nd century. Aboard NX-class starships of that era, a shower stall was a feature of an ensuite bathroom in the captain's quarters. The shower could be operated from a control panel outside the stall. (ENT: "Unexpected", "Singularity")
In 2151, Captain Jonathan Archer was showering in his quarters on Enterprise NX-01 when the artificial gravity went offline, sending him and the water droplets "floating" in the air. (ENT: "Unexpected")
The next year, Sub-Commander T'Pol attempted to clear Captain Archer of a specific kind of mind-altering radiation, which was being emitted from a nearby trinary star system, by washing him under a shower while he was fully clothed in his uniform. She activated the shower from the control panel outside the shower stall and watched from that position. Though Archer immediately asked her to turn the shower off, she waited until it became clear that Archer had regained his mental faculties, then deactivated the shower. (ENT: "Singularity")
In early January 2154, Doctor Phlox hallucinated that the shower in Ensign Hoshi Sato's quarters on Enterprise was being used by her while she was apparently fully clothed and had horrific facial effects of exposure to a trans-dimensional disturbance that, in both Phlox's hallucination and reality, was outside the ship. In Phlox's hallucination, the shower was on a hot setting, as evidenced by it meanwhile producing thick steam. In actuality, however, the shower wasn't even turned on and Sato was lying sedated on her bunk, where she was meant to be. (ENT: "Doctor's Orders")
Later that year, T'Pol had a nightmare in which she imagined herself taking a shower with Charles Tucker III and them kissing with increasing passion, T'Pol at one point pushing Tucker against the shower stall. As the nightmare continued, the imaginary T'Pol eventually became enraged and her face changed to show the horrific effects of trellium-D affliction, moments before the real T'Pol awoke. (ENT: "Damage")
By the 2270s, Starfleet vessels had begun to replace traditional, water-based showers with sonic showers. This was the case right up until at least the late-24th century. (Star Trek: The Motion Picture; TNG: "The Naked Now"; DS9: "If Wishes Were Horses"; VOY: "Juggernaut", "Pathfinder", "Live Fast and Prosper")
In 2370, Ensign Melora Pazlar explained to Doctor Julian Bashir that experiencing low gravity was "like slipping into a hot tub at the end of the day," to which Bashir joked, "I'm a shower man myself." (DS9: "Melora")