To domesticate something is to tame a wild animal or plant so it can live with people. Dogs and cats are called domesticated animals because they live with us peacefully.
Nobody knows who first domesticated a wolf, but whoever it was was a very important person. If people hadn't started living with wolves, slowly domesticating them and teaching them to get along with people, wolves would never have evolved into today's dogs. We usually talk about how to domesticate animals, but wild plants can be domesticated too.