* Stars DO move: All stars are constantly in motion. They orbit around the center of their galaxy, much like planets orbit a star. Our Sun, for example, orbits the center of the Milky Way galaxy.
* We DON'T see them move much: The distances between stars are so vast that their movement is incredibly slow from our perspective. Even over thousands of years, the apparent positions of most stars change very little.
Here's an analogy: Imagine watching a car driving far away on a highway. From your perspective, it might seem almost stationary even though it's moving quickly. The same is true for stars.
So, to answer your question directly: Stars do move, but their movement is difficult to perceive from Earth due to the vast distances involved.
