The point in the sky that corresponds to Earth's North Pole, around which the Celestial Sphere therefore appears to rotate. It is not a fixed point in the sky, but it currently lies close to the starPolaris in Ursa Minor.
A point in the sky that corresponds with Earth's own North Pole. Because this point always lies directly above the Earth's pole, the brightstar that lies close to it, Polaris, always lies due north from an observer's point of view. From the surface of the Earth, it appear that all celestial objects, from the Sun to the stars, rotate around this point once each day. This illusion is due to the fact that it is the observer who is carried round the Earth's own poles by the planet's rotation.
The declination of the Pole Star (its angular distance from the Celestial Equator) is fixed, by definition, at +90°. However, its altitude (the angle it makes with the horizon) is not fixed, but varies according to the latitude of the observer. This is very useful for navigation in the northern hemisphere, since the altitude of the Northern Celestial Pole is always equal to the observer's own latitude: by measuring the Pole's angle to the horizon, it's possible to exactly calculate your own distance from the Earth's equator.
The Northern Celestial Pole is an extension of the Earth's geographic North Pole into the sky. To an observer standing at the exact North Pole of the Earth, the Celestial Pole would appear directly overhead, marked (at present) by the relatively brightstarPolaris in Ursa Minor.
For northern navigators, this measurement is made particularly straightforward by the fact that a bright and easily distinguishable star lies very close to the celestial pole (navigators south of the equator have no such luxury). This star is Polaris, the brightest of the stars in Ursa Minor, which is easily located by the two Pointerstars in Ursa Major. Polaris is presently some 44' (about three quarters of a degree) from the Northern Celestial Pole itself.
Polaris hasn't always been the Pole Star. In fact, it has only been close to the Pole for the last thousand years or so, and over the next millennium it will gradually move further away. This is because the Earth's motion is constantly affected by the pull of other bodies in the Solar System, especially the Moon and the Sun, which causes a 'wobble' in its orbit. This, in turn, causes the Pole to move relative to the stars.
The relative Galactic direction of the Northern Celestial Pole. Because the celestial poles coincide with the Earth's geographic poles, this line also represents the Earth's north-south axis with respect to the Galaxy as a whole.
The effect of this wobble (properly called precession) is that both celestial poles follow a broad circle through the sky. For most of the time, there is no Pole Star at all, but occasionally the Pole will pass near a conspicuous star - we are lucky to live in a time when Polaris fulfils this role. For the ancient Egyptians, the Pole Star was not Polaris, but Thuban in Draco, while observers in the far future will see yet other stars at the Northern Celestial Pole.