A barycenter is the center of mass around which two or more bodies orbit. In a simple system, like the Earth and the Moon, the barycenter is located inside the Earth, but not at its center. This point is where the gravitational forces of the bodies balance each other. In more complex systems, such as the Solar System, the barycenter can shift depending on the positions of the planets and their moons. For example, the barycenter of the Earth-Moon system moves as the Moon orbits, illustrating how gravitational interactions influence the motion of celestial bodies.