what is diff: Class "A", "A/B", and "B"

Class A is non-switching. It produces a full power envelope whether you are using it or not,that's why they get so hot.
Class A/B runs in Class A during low power operation and then switches to Class B for more demanding power needs. Class B amps adjust the power envelope to the power required for the music. Less heat. This is a very simplified explanation, but should give you a general idea.

Sorry you guys didn't like my "power envelope" description.

Amplifier Design Principles

This section will detail design philosophies of amplifiers and the various classes of amplifiers applied in audio. For example:

Class A - transistor amp conducts for the entire cycle of input signal, conduction angle 360 deg. Runs hot, as the transistors in the power amp are on all the time, but has high sound quality.

Class B - positive and negative halves of the signal dealt with by different parts of the circuit, the output devices switching continually. Runs cooler, but the sound is not as pure.

Class AB - biasing the transistor amp at a non-zero DC current much smaller than the peek current of the signal source. Second transistor conducts during negative half cycle of waveform and the currents from the 2 transistors are combined at the load. A compromise between sound quality of Class A and efficiency of Class B. Most amp designs employ this method.

This is a direct copy from the Audioholics web site.