One of the first things that catches the attention of any beginning power meter user is how variable their power output tends to be. This is largely due to the constantly changing resistances (e.g., small changes in elevation, wind,...) that must be overcome when cycling outdoors. Because of this variability, training with a power meter is not directly comparable to training using a heart rate monitor.
This variability means that the overall average power (1) for a workout or race is often a poor indicator of the actual intensity of the effort. This is especially true for races, since power can vary dramatically from one moment to the next as, e.g., a rider first tries to conserve energy and then attacks.
Adapted power (2) is calculated by a special algoritme on your power data that takes into account the variability of power data. This means that workouts with repetitive high-intensity intervals will have a adapted power much higher than the average power of the workout. Therefore, adaptated power is a better indicator than the average power to understand the true metabolic demands of a workout.