In this case, the barycenter is the center of mass of the earth-moon system. Both earth and moon orbit this barycenter/center of mass. If you add more planets, this barycenter will be somewhere else. For the whole solar system, the barycenter is very close to the sun or even inside it. read more
The barycenter (or barycentre; from the Ancient Greek βαρύς heavy + κέντρον centre) is the center of mass of two or more bodies that are orbiting each other, which is the point around which they both orbit. read more
The barycenter, aka, "center of mass", aka, "center of gravity" of the Earth-Moon system is located within the Earth. Due to Earth's rotation and the orbiting of the Moon, the Earth-Moon barycenter is always on the move. read more