The two points (north and south) about which the sky appears to
rotate are known as the celestial poles. They are the
(imaginary) projection of the Earth's axis of rotation into
the sky. If you stand directly on top of either of Earth's
poles, the celestial poles are directly overhead. They serve as part of the reference system of the equatorial coordinate system.
The celestial poles have no physical relevance other than
as convenient reference points for terrestial astronomy and
navigation. In the northern hemisphere, the star closest to the North Celestial Pole is Polaris, α Ursae Minoris, the Pole star,
whose equatorial coordinates are α:02h 31m 49.08s, δ +89° 15' 50.8'' (J2000).
In the southern hemisphere, the faint star σ Octantis is used as the pole star. It has coordinates
α 21h 08m 46.85m, δ -88° 57' 23.4'' (J2000). Because of the Earth's precession, these stars are only the current pole stars. Several bright stars lie close to the North Celestial Pole during the 23,000 year precession cycle, including Vega (α Lyrae), Thuban (α Draconis), and Alderamin (α Cephei).
When using a telescope with an equatorial mount, one aligns the polar axis of the mount with the north or south celestial pole. When the alignment is correct, the
telescope should follow the sky in right ascension without having to adjust the telescope. The celestial poles/pole stars are also used in practical navigation at night, as the direction to the visible celestial pole is the direction of true north or south.
Trivia: Polaris is a variable star, but pretty soon it might not be! It's a Cepheid variable, but the amplitude of its light variations is declining and some astronomers think it might stop pulsating altogether.