An altazimuth mount (aka alt-azimuth mount, altitude-azimuth mount, azimuth-elevation mount) is a straight-forward mount of a telescope on a horizontal axle, in turn, mounted on a vertical axle. The two can provide the means to swing the telescope to any compass direction and raise it to any angle above the horizon. Such a telescope can be termed an altazimuth telescope.
The main alternative is the equatorial mount, which has an axle parallel to the Earth's axis of rotation, so a simple, constant velocity rotation allows it to track objects in the sky. Equatorial mount was once preferred, but being bulkier, makes a significant difference for large telescopes, and with the development of computer control, the coordinated adjustments necessary to track objects similarly same with an altazimuth telescope are easily handled.