Barycenter
The Barycenter is the center of mass of orbiting bodies; all the bodies in an orbiting system will orbit around the barycenter. The barycenter of two bodies can be in the middle of two equal masses, close to a large mass, or even inside a very large mass as is shown in Figure 1.
Figure 1: Different two-body systems with indicated orbits (blue) and barycenters (red).
The barycenter of our solar system lies inside our sun, but not at its center, meaning the sun ‘wobbles’ as it orbits around the solar system barycenter. We observe this wobble around other stars in the universe with a technique called Doppler Spectroscopy which shows that other stars also have orbiting planets.