In astronomy, it's actually the center of mass where two or more celestial bodies (planets or stars etc.) orbit one another.
In most cases the celestial bodies are not exactly the same size and therefore the barycenter is not always exactly in the center of the largest of those bodies.
A very good example of this is Jupiter and the Sun. Jupiter is the largest planet in our solar system.
It's also known as the gas giant. It's heavier than all the planets combined. But even with its great mass, it still only weighs one one-thousandth as much as the Sun!
This means the Sun is the major mass in the orbit between the Sun and Jupiter. The barycenter between the sun and Jupiter is located outside the sun. The distance it is located at outside of the sun is 7% of the radius of the sun.
This may not seem like a lot, but you can easily fit the Earth and two of Earth’s moons into that distance and still have a bit of space left. Compared to the size of the Sun and Jupiter however, that 7% is actually not a lot at all – it's only 15,114.85 miles.
