The night sky appears to turn, stars rising in the east and setting in the west (the opposite is true for observers in the Southern Hemisphere). Of course, it's not the sky that's turning, but the Earth.
In the Northern Hemisphere, the sky seems to rotate around Polaris, the North Star, which appears to remain motionless. Polaris is the "pivot point" around which the other stars move.
Click here to zoom in, and you'll see that Polaris is not really motionless. It travels in a circle like any other star. The true pivot point is the north celestial pole, the point in the sky directly above the Earth's north pole.
Polaris is about a degree away from the north celestial pole—pretty close. It traces a circle around the north celestial pole one-and-a-half degrees in diameter.