Yes, stars are appear moving. Our galaxy like all other spiral galaxies is rotating. The stars move on orbits around the centre of the galaxy. It was the motions of stars in external galaxies that lead to the idea of dark matter in the universe. Stars also have some random motions. They do not orbit galaxy in exact circles.
As observers we see this motion of the stars as what is called proper motion, the projection of their velocity on to the plane of the sky is radial motion. Normal Answer : Alternate answer is No. All the stars appears that they are moving because of rotation of earth.