Your fun fact of the day: Jupiter is so massive that rather than orbiting the Sun, they both orbit a point in space between them.
In the case of the Earth and the Sun, both bodies orbit around the very center of the mass (similar to center of gravity) between them. This point is called the "barycenter."
Earth and the Sun are "connected" by the gravity pulling them together. It's just like the light end and heavy end of the sledge hammer. Compared to the size of the Sun, though, Earth is about like a flea on a cat! So the center of mass between the Earth and the Sun is almost—but not quite—the very center of the Sun.
Jupiter, on the other hand, is 318 times as massive as Earth. Therefore, the barycenter of Jupiter and the Sun is a bit further from the Sun's center. So, as Jupiter revolves around the Sun, the Sun itself is actually revolving around this slightly off-center point, located just outside its surface. So, they actually rotate somewhat like this: