What do you want the computer for?

Some possible things that they track, depending on the computer:

Current speed
Average speed for the ride
Maximum speed for the ride
Cumulative distance for the ride
Odometer (cumulative distance for all rides)
Current time
Elapsed time of ride
Current cadence
Average cadence for the ride
Maximum cadence for the ride
Current heart rate
Maximum heart rate for the ride
Est. calories burned
Altitude
% grade of current climb
Total feet climbed/descended for the ride
GPS tracking of your position
Ability to download routes from websites like mapmyride or ridewithgps
Ability to set goals for things like speed and heartrate
Ability to upload ride data to a website to analyze rides

etc etc

A basic cycle computer will track speed and distance for your ride, and will probably include a clock and total ride time.

More advanced computers can track cadence (usually the cadence sensor is an additional purchase) and include heart rate monitors.

GPS-enabled computers add lots more features.

Whatever you choose, read the specs carefully to make sure it keeps track of the things you care about. I bought an inexpensive computer for my mountain bike last year without realizing it did not compute average speed for the ride -- I had to do it myself based on the total ride time and total distance.