Watts is (not are) a function of Voltage x Current.(Amperes)
so V x A = W
Now your volume control on your amp changes the voltage that is applied to the speaker terminals. For a given voltage, an amount of current will be "drawn" depending on the resistance or impedance of the speaker.
where A = V/R
If the speaker load os 8 Ohms, then at lets say 16V this means that the amp has to deliver 2 amps, which means it needs to be able to produce 16x 2 watts = 32 watts.
Now if at that same voltage our speaker has the same sensitivity, but this time its impedance drops to 4 ohms then the amp has to be able to deliver 4 amps of current, or 16 x 4 = 64 watts. Some "difficult" speakers may even present a 2 ohm load at some frequencies, so suddenly you need 128 watts, all just to maintain the same "loudness" setting. In effect, using watts as a measure of an amps loudness capability is only part of the story, which is why you also need to know its max current capabilty, measured as steady sate and short term peak. Therefore, there is some mileage in the view that you can never have too high a power rating, but then again it is perfectly possible to match a low powered amp to the right speakers and make a lot of noise, where thos speakers are both sensitive, and also are a easy load (i.e dont drop much below the nominal 8 ohm impedance).