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")