Most people associate power with muscles and muscle strength - the larger the muscles, the greater the power. This is only partially true. Smaller muscles that are properly toned can generate larger amounts of power than larger muscles that are not properly toned. This is why athletes that appear small may still be capable of great feats of strength and stamina.
Power is the rate at which work is done. The greater the power, the more work that can be done. In sports, the more power that the athlete can generate, the faster, farther, higher, etc., the athlete can go. Ultimately, the amount of power the athlete can generate goes back to how, and how much, the athlete trains and prepares for that particular sport.
Power is measured in watts. The best known reference to watts is with the light bulb. The greater the number of watts a light bulb can generate, the brighter the bulb. The greater the number of watts an athlete can generate, the stronger they will be in sports. The greater your level of fitness, the faster you should be able to run up the stairs or hill, thus the greater the amount of watts of power that you can generate.