The equatorial coordinate system is probably the most widely used celestial coordinate system. It is also the most closely related to the geographic coordinate system, because they use the same fundamental plane, and the same poles. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, projecting the geographic poles onto the celestial sphere defines the north and south celestial poles.
However, there is an important difference between the equatorial and geographic coordinate systems: the geographic system is fixed to the Earth; it rotates as the Earth does. The equatorial system is fixed to the stars (actually, the equatorial coordinates are not quite fixed to the stars. See precession - also, if hour angle is used in place of right ascension, then the equatorial system is fixed to the Earth, not the stars), so it appears to rotate across the sky with the stars, but of course it's really the Earth rotating under the fixed sky.
The latitudinal (latitude-like) angle of the equatorial system is called declination (Dec for short). It measures the angle of an object above or below the celestial equator. The longitudinal angle is called the right ascension (RA for short). It measures the angle of an object east of the vernal equinox. Unlike longitude, right ascension is usually measured in hours instead of degrees, because the apparent rotation of the equatorial coordinate system is closely related to sidereal time and hour angle. Since a full rotation of the sky takes 24 hours to complete, there are (360 degrees / 24 hours) = 15 degrees in one hour of right ascension.
This article originates from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml