Domesticated means trained to live or work for humans, i.e. pets and farm animals. For centuries humans have believe that dogs are domesticated wolves, but DNA testing reveals that they are in fact a different species.
Domesticated comes from domus, the Latin word for home, which is easy to remember — instead of a "roof over our heads" think of your "home as a dome." Domus gives us not only domesticated (adapted to the home or the farm), but also domestic (cooking and cleaning are "domestic" chores), a domestic (someone like a maid who works inside a home as a paid employee), and domicile (a building that serves as a home). Thus domesticated means an animal tamed to live in your home — or, as some women like to joke, a man.