Bike Computers

Wireless
This is the ability for a computer's sensor to broadcast its signal via radio frequency to the computer on your handlebars. This is very helpful to mountain bikers, who quite regularly have branches reaching out and grabbing the cables on their bike. Road riders like them as well because they are easier to set up and ultimately are simple and clean looking.

If you ride with a group of people, like in a race, then it might be a good idea to get a unit with a coded signal so you don't pick up other signals accidentally.

Heart Rate
Heart rate sensors are normally on a strap you wear across your chest that broadcasts heart beat info to the computer. These allow you to maintain a certain level of constant exertion, which tends to be the most effective way to work out.

Speed and Distance
Virtually all computers keep track of speed (mph) and distance (miles or meters).

Cadence
A cadence sensor typically installs on your crank arm and keeps track of the rotations your legs make per minute. Experienced road racers will tell you that it is good form to keep a consistent cadence over all speeds.

However, for most mountain bike riders, this isn't a problem because pedal cadence is often dictated by terrain to give the rider more clearance for going over roots, etc.

Power
High end bike computers can sometimes compute power by measuring speed, cadence, and chain tension. This is important if you need to know how different slopes and conditions effect your ride.

GPS
Some high end units also incorporate GPS to their computers, and often supply you with a program that tells you how you are performing at every spot on your ride when you upload your ride data to it. This is great for going over your ride with a fine tooth comb (or an alibi if you require one).