"Eppur si muove." — Galileo Galilei
Even though the famous utterance is likely apocryphal, we have, nonetheless, known for hundreds of years that the Earth revolves around the Sun. And while Earth’s orbit does completely encompass the Sun, technically, the point around which the Earth revolves is not the Sun. Rather, it is the center of mass of the Solar System — called the barycenter.
All the objects in the Solar System have mass and, therefore, generate a gravitational effect on all the other objects in the Solar System. This means giant Jupiter and tiny Mercury (and even non-planet Pluto) all pull on the Sun, and each other. The combined effects of all the gravitational effects means that the center of mass of the Solar System is not the center of the Sun.
The barycenter is sometimes close to the center of the Sun, and, oftentimes, it is within the Sun. Depending on the position of the planets, however, it is frequently not actually located within the Sun. At these times, the Earth, in a manner of speaking, does not revolve around the Sun.