The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This conveniently divides the sky into the upper hemisphere that you can see, and the lower hemisphere that you can't (because the Earth is in the way). The pole of the upper hemisphere is called the zenith. The pole of the lower hemisphere is called the nadir. The angle of an object above or below the horizon is called the altitude (Alt for short). The angle of an object around the horizon (measured from the North point, toward the East) is called the azimuth. The horizontal coordinate system is sometimes also called the Alt/Az coordinate system.
The horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object changes with time, as the object appears to drift across the sky. In addition, because the horizontal system is defined by your local horizon, the same object viewed from different locations on Earth at the same time will have different values of altitude and azimuth.
Horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an object has altitude=0 degrees, it is either rising (if its azimuth is < 180 degrees) or setting (if its azimuth is > 180 degrees).
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