A cycling watch is typically a GPS watch with complete and accurate GPS functions.
Occasionally, they can be watches that wirelessly connect to a speed and cadence sensor. These watches will help you accurately measure speed and distance, along with heart rate and other functions. Some have built-in barometers that act as an altimeter to measure altitude gained and lost.
The intent of a cycling watch, or a triathlon watch, is to assimilate an enormous amount of information on the fly so that an athlete can adjust variables to improve their performance.
Since tempo and cadence are such critical variables to setting a pace that can last for hours on end it is critical to know information like pedal revolutions, minutes per mile, average speed, and power. All of these become critical variables that act like a car's tachometer on the engine that is your body. Knowing how fast to rev the engine, and for how long is critical to how long the engine can last at a specified area of output. These are the tricks that the world-class athletes master. They have an intimate understanding of where their anaerobic threshold is and they are always operating just barely below it.