C.V., the reason that an amplifier has a different wattage rating when driving different impedance speakers is simply because, as John B. points out, when the impedance of the speaker is lower the amp can put out more power, so there's a number given which was measured when it was tested in the lab with the lower impedance load.
An amp has a given amount of gain that it applies to the signal coming in from a CD player, etc. The stronger the incoming signal(which can be raised or lowered depending on the volume control setting), the more power is output; it doesn't matter what the capability of the speaker to handle power is. Keep in mind that regardless of what the maximum power rating of an amp is, a comfortably loud average listening level needs an output of only about 1 watt and even on brief peaks the maximum power capacity of a very powerful amp will probably never be used.
