Domestication was the adoption and breeding of a species of wild animal to enable it to form a relationship with people, either for livestock or companionship purposes. It could also refer colloquially to a person settling into married life.
In 2154, after Jonathan Archer expressed surprise that T'Pol had ever had a seh'lat as a pet, T'Pol confirmed that hers was domesticated and smaller than the one they'd just encountered in Vulcan's Forge. (ENT: "The Forge")
In 2372, Chakotay doubted that a monkey found on New Earth could be easily domesticated. Believing they would be remaining on the planet until their deaths, Kathryn Janeway replied they had the rest of their lives to try. (VOY: "Resolutions")
In 2375, shortly after the wedding of the Silver Blood USS Voyager's "B'Elanna Torres" and "Tom Paris", "Harry Kim" asked "Paris" if he was hungry. "Paris" declined joining him for a meal, saying he had dinner with "B'Elanna". "Kim" then quipped, "Married one day and you're already domesticated." (VOY: "Course: Oblivion")