The barycenter (or barycentre) is the point between two objects where they balance each other.
For example, it is the center of mass where two or more celestial bodies orbit each other. Let's consider the Earth-Moon system:
The barycenter of the Earth-Moon system is a point in space about which the Earth and Moon appear to orbit as they travel together around the Sun. It is located exactly along the line that connects the center of the Earth with the center of the Moon.