Here's an article from Electronic Design that talks about the advantages of running a Class D amp when compared to other amplifier designs with regard to power efficiency.
They explain that an amplifier works by applying a voltage of alternating polarity to a loudspeaker, driving it back and forth to move the air that produces the sound. The amp basically has 2 power rails for the + and - polarity voltages.
With a Class A amp, both switches are on simultaneously to create the required voltage, so they're only about 15% efficient. This means that only 15% of the power is used to drive the speakers. The other 85% is lost as heat. That's why the higher power (over 100W) Class A amps are usually pretty large and include massive heat sinks. With Class B amps, only one switch is on at a time, resulting in efficiencies of around 75%. Unfortunately the trade off is poorer sound quality. Class AB is a combination or compromise between A and B with both switches on simultaneously, but the non-load carrying rail was only minimally on. This improved the sound, but only resulted in efficiencies of about 30% due to switching losses. The Class D amp does this by switching these voltages on and off. With the Class D amps, the switching losses are very low resulting in an overall efficiency of more than 90% with very good sound quality.
Read the article if you are interested in more of the details.