Astronomers often use telesopes to view very distant and faint objects. This can mean leaving the CCD exposed to the sky for many seconds or minutes, or even hours in some cases. As the Earth rotates, stars in the sky appear to move. Telescopes have to be able to compansate for this motion. Otherwise stars and other objects would appear as streaks in an image, rather than as points of light.
The most common type of mount for small telescopes is the equatorial mount. It works by having one axis aligned to the Earth's celestial pole, which is parallel to the axis of the Earth's rotation. It then uses a motor to to make the telescope slowly rotate about that axis at just the right speed so that when the telescope is pointed at an object, that object stays centered in the field of view.
LCOGT's 0.4 and 1.0 meter telescopes use a type of equatorial mount called a C-Ring mount.
The animation below shows a schematic of an LCOGT 1m telescope responding rapidly to a request for observations. The telescope slews to the target and then tracks it.
Altitude-azimuth or altazimuth mounts are usually prefered for larger telescopes because they are easier and cheaper to build for a massive telescope than an equatorial mount would be. Altitude-azimuth mounts have two axes, a vertical and horizontal, that the telescope can rotate on. Both axes must move at variable rates to in order to compensate for the Earth's motion and keep the orientation of the field of view from rotating. This is complicated and normally done using a computer guiding system.
LCOGT's 2.0 meter telescopes use altitude-azimuth mounts.