The official definition of a planet is an object of a certain size that forms in orbit around a star but isn’t big enough to become a star itself, so (barring accidents) planets nearly always still orbit their more massive ‘parent stars’, and because the less massive object is usually said to orbit the heavier one, the planet always revolves around the star. However, there’s a slight complication. In reality the two objects actually orbit around their shared ‘centre of mass’, or barycentre (normally well inside the star). Although the star isn’t really revolving ‘around’ the planet, it is being pulled around by it, and the resulting ‘wobbles’ are one of the clues astronomers seek to discover new planets.
Answered by Giles Sparrow.