Watts and power

Can somebody break it down in layman's terms for me? Why is it that sometimes an amp that has a high watt rating (like, say, a lot of class D amps do) don't seem to always have the balls that much lower rated A or AB amps do? I have heard some people say, "It's not the watts, it's the power supply." Are they talking about big honkin' toroidal transformers? I know opinions vary on a speaker like, say, Magnepans - Maggies love power, right? A lot of people caution against using class D amps to drive them and then will turn around and say that a receiver like the Outlaw RR2160 (rated at 110 watts into 8 ohms) drives Maggies really well! I'm not really asking about differences between Class D, A, or AB so much as I am asking about how can you tell the POWER an amp has from the specs?