A more involved mechanism, designed to track the motion of the stars by turning on a single axis, is termed an equatorial mount.
On some mounts the scope swings left and right, up and down, just as it would on a photo tripod; these are known as altitude-azimuth (or simply alt-az) mounts. Many reflectors come on an elegantly simple wooden platform, known as a Dobsonian, that's a variation of the alt-az mount. A more involved mechanism, designed to track the motion of the stars by turning on a single axis, is termed an equatorial mount. These tend to be larger and heavier than alt-az designs; to use an equatorial mount properly you'll also need to align it to Polaris, the North Star.