A barbershop was a place where individuals, particularly males, went to have their hair cut, shaved, or styled by a barber. Barbershops were sometimes identified by a barber pole. (TOS: "The City on the Edge of Forever")
Federation starships like the USS Enterprise-D had barbershops, where crewmembers could get a haircut, get their beards trimmed, have their sideburns stylized in accordance with Starfleet standards, or enjoy a relaxing cosmetic application.
The barbershop was a pentagonal room with seats for up to four customers. It featured a small waiting area with comfortable chairs and nice wall decorations.
The room was equipped with everything expected from a barbershop: many mirrors (evoking the Federation's LCARS style interfaces), washbasins, and even two long displays with stylized versions of the ancient barber's pole were present, interwoven with the Starfleet-arrowhead.
Though many high-tech devices were employed in the shop, including electronic devices used to trim sideburns, dye hair or color toenails, old-fashioned scissors were also present.
The barbershop aboard the Enterprise-D was run by the Bolian barber Mot, "the best barber in Starfleet", befitting the Federation's flagship. At least three more Bolian barbers worked at the barbershop, including V'Sal. Two male Humans (one named Setti) and a Human female were also among Mot's staff. All crewmembers working in the barbershop wore a special uniform consisting of a black undershirt and a cape with a characteristic striped pattern made from an orange and blue fabric.
When Samuel Clemens saw a Bolian working at the barbershop in a corridor, he was of the impression that he had been brought to the ship as a servant, but Counselor Deanna Troi quickly explained to the visitor from the 19th century that the barber was on the ship on his own will. (TNG: "Time's Arrow, Part II")
Most of the senior staff of the Enterprise-D visited the barbershop regularly, keeping Mot up to date about the latest happenings in the Federation.
Shortly before the marriage of Miles O'Brien and Keiko Ishikawa in 2367, Geordi La Forge paid a visit to the barbershop to get a haircut by V'Sal, though he had only been there a week earlier. Data visited the chief engineer at the barbershop, a rare visit, as his hair didn't require trimming. (TNG: "Data's Day")
A little later that year, both Counselor Troi and Doctor Beverly Crusher enjoyed some relaxing beauty treatments in the barbershop; Crusher was especially satisfied with the soothing colgonite astringent. (TNG: "The Host")
In early 2368, Captain Jean-Luc Picard had his hair cut by the always inquisitive Mot, who was very keen to describe his views of the current Cardassian situation. Commander William T. Riker had been to the barbershop just a day earlier and agreed a hundred percent with the Bolian's evaluation. (TNG: "Ensign Ro")
Roughly one year later, Lieutenant Worf paid the barbershop a visit for his regular haircut and beard-trimming. He made very clear that Mot was not to cut off as much hair as he had during his last visit. It was in the barbershop, when seeing Mot's scissors, that Worf realized something was wrong, which, as it later turned out, had to do with an abduction by solanogen-based lifeforms. (TNG: "Schisms")
Finally, when trying to explain his unauthorized presence in a cargo bay, the Ferengi Qol claimed that everything was just a misunderstanding and he got lost on his way to the barbershop and ended up in the cargo bay, a lie not hard to see through taking into account the sparse amount of a Ferengi's hair. (TNG: "The Perfect Mate")