A 24 hour day may seem long when you're waiting in line at the store, but the earth's spin appears startlingly fast in a telescope. The job of a equatorial mount, like our Losmandy GM 200, is to track the stars as the earth spins. As long as the drive system is on, a small motor will drive the telescope so that stars appear stationary.
    There are several options for controlling the drive speed. In star mode, the motor spins steadily at the sidereal rate. In king mode, the drive speed takes into account the refraction from earth's atmosphere. They are very similar. Lunar and solar rates allow you to track the moon and sun.
    In addition to tracking the sky, the drive system allows you to control small telescope movements with a computer or the hand paddle. The rate at which the motors spin is controlled by the (G/S) setting. 0.3X and 0.5X tend to be too slow for movement or autoguiding. 2X is the optimum rate for computer-controlled autoguiding. Faster rates can be useful for hand paddle movement, but they are not necessary because the hand paddle has a special feature: hold the button you want to go and press the opposite button at the same time and it will go at 16X. It is best to stick with one rate for the whole night because the computer is calibrated for a specific rate. For reference, 1X is the rate of the earth's spin (ie. the tracking speed).

A more complete description is available here, but it is technically for a different mount.