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.