The Watt is a measure of work , or how much work something can do. It is actually quite analogous to horsepower, and you physics buffs know that both use the same units. The mechanical analogy of horsepower works well for imagining a Watt as well. You don't need horsepower, you need torque.
Musical signal is a start and stop type of drive.
So for good sound, an amp needs to be able to push the woofer out, then stop it, reverse it, and pull it back, many times per second. The tough part is actually the stopping and reversing, not getting going full speed. Watts are hard to measure, or so it would seem, since different companies seem to get such different results. Who cares, because you can bet the big boy won't sputter into hard to drive speakers. In reality, wattage ratings are only comparable between similar price point components, and even then you really should not be stuck on this spec.