The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to an observer at the Earth's North Pole and South Pole, respectively. As the Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other points appear to rotate around them, completing one circuit per day (strictly, per sidereal day).
The celestial poles are also the poles of the celestial equatorial coordinate system, meaning they have declinations of +90 degrees and −90 degrees (for the north and south celestial poles, respectively).
The celestial poles do not remain permanently fixed against the background of the stars. Because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The Earth's axis is also subject to other complex motions which cause the celestial poles to shift slightly over cycles of varying lengths; see nutation, polar motion and axial tilt. Finally, over very long periods the positions of the stars themselves change, because of the stars' proper motions.
An analogous concept applies to other planets: a planet's celestial poles are the points in the sky where the projection of the planet's axis of rotation intersects the celestial sphere. These points vary because different planets' axes are oriented differently (the apparent positions of the stars also change slightly because of parallax effects).