The barycenter is the common center of mass that two orbiting bodies — a planet and its moon, or two stars in a binary system — actually revolve around.
The barycenter is the common center of mass that two orbiting bodies — a planet and its moon, or two stars in a binary system — actually revolve around. If one body is much more massive, the barycenter sits close to (or even inside) it; if the masses are similar, it sits somewhere between them.
Earth (5.97×10²⁴ kg) and the Moon (7.35×10²² kg) are separated by 384,400 km. Distance from Earth's center to the barycenter = (7.35×10²²/(5.97×10²⁴+7.35×10²²)) × 384,400 ≈ 4,671 km — actually inside the Earth.
It's the common center of mass that two orbiting bodies (like a planet and its moon, or a binary star system) both orbit around.
It's a weighted average of the two bodies' positions based on their masses: the barycenter sits closer to the more massive object.
Not always — for very unequal masses (like Earth-Moon) it usually is, but for more similar masses (like some binary stars) the barycenter can sit in empty space between them.