A Barycenter in Universe Sandbox is a simulated object representing the barycenter, or center of mass, of two or more objects interacting via gravity. This center of mass exists for any two or more objects with mass, but the simulated Barycenter object allows the user to see and manipulate the barycenter.
If two objects have equal mass, their barycenter will be located exactly between them. Otherwise, the barycenter will be closer to the more massive object. In systems where one body is much more massive than the other (for example, the Earth orbiting the Sun, or the Moon orbiting the Earth), the barycenter will be located inside the larger body, making it appear as if the smaller object is orbiting the larger object, rather than their barycenter.