While Jupiter does revolve around in an oval-shaped orbit, just like the rest of the planets, the central point of that orbit is not the sun. Jupiter throws its weight around in the solar system, affecting the sun itself, so there’s a tug-of-war that has both bodies revolving around the barycenter, a point just above the surface of the sun.
The sun is about 1,000 times more massive than Jupiter, and these two bodies affect one another proportionally, so the amount Jupiter's gravity pulls on the sun is one-thousandth the amount the sun's gravity pulls on Jupiter. And Jupiter's orbit takes 11.8 Earth years to compete, and the sun travels around the barycenter takes the same amount of time.
The explanation is pretty cool, but the part about using this knowledge to study other stars and their possible planets we can’t see is …out of this world!
(Animation credit: NASA)
And it isn't just about size, but for a given parent body, size times distance. If the Earth were 1500 times further from the Sun, the Earth+Sun barycenter would be above the surface of the Sun. If Earth's Moon were about 40% further away, the Earth+Moon barycenter would be above the surface of the Earth, while if Charon were about the half the distance to Pluto, its barycenter wouldn't be above the surface of Pluto. You could also have an elliptical orbit where the barycenter moves between being inside and outside of the larger object.
It was again raised during the famous flyby, so I thought everyone else knew about it.