When is Cyclometer useful?
Speedometer = device which measures speed.

Odometer = device which measures distance traveled.

Cycle computers can normally do both (plus many other features you may or may not need).

Are they absolutely necessary for cycling?  No, but they can be quite helpful in many cases.  When riding long distances (e.g. touring, randonneuring), it's often important to know how far you've traveled, so an odometer comes in handy.  You may be trying to determine where you are on a map, how far until the next turn, how far to the next town, etc.

If you're training, being able to track your performance over time can also be handy.