Privacy was the ability to keep some of one's experiences and life from others.
According to Captain Jonathan Archer, dating wasn't discouraged aboard Enterprise NX-01 but there wasn't a lot of privacy. He answered this to a question from Geoff Miles in 2151. (ENT: "Breaking the Ice")
During the 23rd century, on Starfleet ships when particularly private conversations needed to be had, the captain had the ability to order the ship's computer to observe their privacy. (DIS: "The Vulcan Hello")
In 2367, the con artist styling herself as "Ardra" attempted to seduce Captain Jean-Luc Picard in his quarters. He attempted both to activate an intruder alert and to contact the USS Enterprise-D's bridge, but neither attempt was successful and she told him that she had arranged for a bit of privacy. (TNG: "Devil's Due")
That same year, Lieutenant Commander Geordi La Forge disconnected both the audio and visual pickups inside the Enterpise-D's conference room so that Reginald Barclay could not monitor the senior staff after he had created a neural scan interface which transferred much of his higher brain functions into the starboard computer core. (TNG: "The Nth Degree")
The Cairn, a telepathic species, did not understand the concept of privacy, as nothing among them was hidden. In 2370, when Maques detected a part of Lwaxana Troi that was "dark," her daughter Deanna Troi initially believed mistakenly that Maques was referring to privacy, not realizing that he had sensed her mother's metaconscious, in which she had suppressed her memory of her lost daughter Kestra. (TNG: "Dark Page")