Mount

A mount is a structure that holds the telescope in place and is often capable of precisely moving the telescope towards the desired target. Some are motorized while others have special slow-motion levers to counteract the rotation of the earth. There are a number of different mount types, this page list the most common used by amateur astronomers.

Altitude/Azimuth
The simplest type of mount, often comes with a 'beginners' telescope. It can move up and down (altitude) and move left and right (azimuth), much like a standard photographic tripod or a gun turret. Motorizing this type of mount is difficult due to the way the earth moves relative to the stars. It is possible but both axis need to be motorized and move at varying speeds, depending on the area of sky the telescope is pointed at. Note that this does not apply if you live on the north/south pole or on the equator. It is possible to construct a mount that only requires a single axis to be motorized, these are equatorial mounts.

More information, as well as example images, can be found at the wikipedia article.

Equatorial
These behave similar to an Alt/Az mount however they are tilted at an angle equal that of it's current latitude. For example, London has a latitude of roughly 51 degrees. This means that an equatorial mount in london should be tilted at 51 degrees with one of the axes pointing towards polaris or pole star (Polaris is a star almost exactly on the celestial north pole - Every other star appears to circle around it). When both of these conditions are met the telescope behaves as if it's situated on the north pole and only one axis needs to be motorized for the telescope to track the sky properly.

More information and example images can be found at the wikipedia article.

German Equatorial
Functionally identical to a normal equatorial mount, but this design is more compact.

More information can be found at the wikipedia article.