Bicycle computers are electronic speedos that tell you a lot more than how fast you're going.
How They Work. In general they work via a sensor mounted on the fork which senses the passing of a magnet mounted on a spoke, sending a signal to the head, which has the wheel size programmed into it so it can calculate speed etc.
What They Tell You. Most computers will tell you your current speed, your maximum speed for this ride, your average speed for this ride, your distance for the ride, your total distance (odometer), your ride time and the time of day. Some will tell you less than this, some will have a variety of other functions ranging from calorie consumption to altitude.
Rear Wheel Mount. For use on a training stand (with a stationary front wheel) you'll need a rear wheel sensor and a long wire kit to suit. The cateye Astrale offers this, as well as cadence (the speed at which you're turning the pedals).
Wires and Transmitters. Some computers have tougher than usual wires in them to prevent damage from catching on bushes etc, and the next step in this direction is the cordless computer which sends the signal from the sensor to the head via a radio signal. No more broken wires, no more ugly wires hanging on the bike, and, in Cateye's case at least, no contacts between a handlebar bracket and the computer head to wear out after years of use on bumpy roads, or to give a poor connection during wet weather.