Like the Sun, the stars move in the night sky. For proof of this, go out on any clear night and look up, noting the positions of a few bright stars, then go back inside for a few hours. Later in the night, go out again and, guess what, the stars have shifted position.
So, how does this work?
The most important thing to understand is that the sky itself does not move, the Earth moves and the motion of the sky is only apparent. So in technical terms, referring to “sunrise” or “sunset” is incorrect as the Sun doesn't move. The motion of the Sun, and other stars, is caused by the rotation of the Earth. The Sun and Stars are all at fixed points in space and the Earth is not. For an easy comparison, stand in a room and twirl around. By doing this, you are simulating the relationship of Earth to the stars. You are the rotating Earth and everything in the room is a star. Objects in the room appear to move even though you know they are stationary, only you are actually moving. The situation is the same for the Earth and stars. Ironically, despite knowing this fact for hundreds of years, we still have yet to adopt it into our daily language.
If you go outside and observe the location of the Northern stars over the course of a night, you will notice that they revolve around a single point in the sky. The question quickly becomes “why?” The answer is simple. The Earth is surrounded by stars in all directions. Imagining a giant arrow starting at the Earth's South Pole, extending through the core of the planet, to the North Pole, and out into space. The North Celestial Pole lies directly overhead of the Earth where the head of the arrow is pointing. In a modification of the experiment in the above paragraph, twirl yourself around in a room looking straight up at a fixed point on the ceiling. The point you are looking at will remain stationary and everything else you see will seem to revolve around that fixed point. The same exact thing happens with the Earth. In fact, every star revolves around the Celestial Pole, but those stars that are far enough away from the pole, out of the circumpolar region of sky, appear to rise in the East and set in the West. Over the South Celestial Pole, the same thing happens as in the North.