By Newton's law of gravity, all objects attract one another. Stars are not fixed in their positions. Because of the great distances between them, they appear to be 'fixed' in the celestial sphere even though they are moving.
Celestial objects travel along their own orbits under the influence of gravitational pulls.
Occasionally they collide. A recent example was the collision of Comet Shoemaker-Levy with the planet Jupiter in July 1994. The comet was originally in orbit around the Sun. Thus, when the comet again came close to Jupiter in mid-July 1994, over twenty fragments of the comet collided with Jupiter.