Since the earliest times in recorded history, the question of around which astronomical body the Sun revolves has been a point of contention amongst astronomers, scientists, and laymen. Even today, many people still mistakenly believe that the Sun revolves around the earth or its own axis. The question of what the Sun revolves around, however, has two correct answers based on the definition of the word revolve. The Sun revolves around a point in our solar system called the barycenter, which is the center of mass of the solar system, as well as revolving around the center of our galaxy, the Milky Way.
The word "revolve" refers to the motion of one object around another object or around a point. It is similar to and often used interchangeably with and confused with "rotate," but in astronomy, the two words have different meanings. Rotation describes the spinning of an object around a line passing through the object called an axis. "Rotate" is another word for spin. "Revolve" means to orbit. The Earth rotates on its axis, but revolves around the Sun.
The center of mass of a system of astronomical bodies is called the barycenter. This is the point around which all the planets and other bodies in our solar system, such as comets and asteroids, revolve. The gravitational attraction between the Sun and the other objects in the solar system causes the Sun to revolve around the barycenter. This movement is very slight when observed in the context of the entire solar system, so slight in fact that in models of the solar system showing the movement of the planets around the Sun, the Sun's own revolution around the barycenter is essentially indistinguishable since the barycenter is very close to the center of the Sun itself.
The Sun and the solar system also revolve around the center of our galaxy, the Milky Way. The period of this revolution is extremely long, taking approximately 200 million years. No one is certain of what lies at the center of the galaxy, however, so this aspect of the question of what does the Sun revolve around has no clear answer. Many astronomers believe that at the center of many galaxies, including our own, are huge black holes, but this theory has not been proven.