Pedaling power is the amount of torque (turning force) exerted on the pedals or the rear hub multiplied by speed or angular velocity.
Power = Force x Velocity
Power is the capacity to do work and bring about change (energy). To create power the rider must push harder (torque) and/or pedal faster (angular velocity). Just like weight is measured in pounds, power is measured in watts. Riding at 100w is equivalent to the amount of power it takes to light a 100w light bulb and keep it lit. Some athletes are more powerful than others because more powerful athletes can do the same amount of work in less time, more work in the same amount of time, or more work in less time.
There is also a distinction between having power (potential energy) and producing power (kinetic energy). Think about the water atop a dam. This body of water that is being held back by the dam wall has potential energy. When the water is allowed to flow through the dam the water loses potential energy but gains kinetic energy. However, if too much water is released quickly the water behind the dam will not have an opportunity to replenish. In an endurance event, it is important to control the amount of energy used and conserve that energy so you get the maximum and consistent power output during the entire event.
Power, unlike heart rate, is the actual exercise stimulus that is not typically changed by internal or external factors. Heart rate is a response to a stimulus and can be distorted by many factors. Power is an instantaneous direct measure of mechanical work while heart rate is a response and predictor of training stimulus that takes several seconds to respond. It is also important to note that power is dynamic and subject to change whereas heart rate has a genetic limit. Heart rate is a component of training but power is the trainable component.
The benefit of using power allows the athlete to quantify his/her work by establishing honest baselines and peak power values. This valid and reliable data leads to precise comparisons to show progress and determine training requirements. This type of information is invaluable to an athlete and coach!