I have long thought that Soundstage reviewer Greg Weaver's concise explanation regarding this question, taken from his 1997 review of the Clayton S-70 amplifier, was one of the most easily digestible for the technically innocent that I've read.
This is the relevant passage taken from Soundstage's website archives (edited very slightly by me for transposition here):
"A brief explanation of amplifier types, and their operational modes: There are two basic types of power amplifiers today, the Push-Pull and the Single Ended designs. These terms apply to the methods of operation used with the power output devices in order to achieve the final signal amplification. With the Single Ended variety, one transistor (or a group of transistors working together) is used to reproduce the entire output waveform. In the Push-Pull method, two separate transistors (or groups of transistors working together) are used to reconstruct the signal. One of each of the devices (or group of devices) is then responsible for only one half of the resultant output waveform. Because the majority of todays audio amplifiers [are of the push-pull variety], I will limit the rest of the discussion to the methods, or classes, of operation for that particular design.
Picture a sine wave. Got it? Good. Now, envision a horizontal line running directly through that sine wave at exactly the vertical mid-point, now referred to as our null point. We now have the top one half of the waveform, or the crests, residing above the horizontal line. The bottom one half of the waveform, the troughs, reside below our imaginary null point, the horizontal line. In the Push-Pull design, one of the two transistors (or groups of transistors) is responsible for reproducing that top half of the waveform and the other, its complement, is responsible for reproducing the lower half of the waveform. In other words, one complement recreates the crests and the other the troughs. Which complement is on and which is off at any given time is determined by where the drive signal is, in relationship to that null point. Above the null point (our imaginary line running horizontally through the full sine wave), and the Push complement is in its duty cycle. Below our null point, and the Pull compliment is in its duty cycle. Now we can look at how the power for each half of the waveform is managed, which will describe its method, or class, of operation.
Class B amplifiers are typified by having one of the complements, responsible for only one half of the full output, turn on only during its duty cycle. It then turns completely off when it is done reproducing its half of the output and rests while the other complement runs through its duty cycle. When that second complement is finished, and the drive signal swings back past the null point into the first complements half of the waveform, it then switches back on again. In other words, each complement is only on when the audio drive signal requires it to be. It then switches completely off as soon as it is done with its half of the signal.
In class A amplifiers, both halves of the complement are on all the time. This means neither half of the Push-Pull complement ever shuts off nor throttles back from full current draw, even during the half of the cycle that it is at rest. This is achieved by the application of a forward bias current applied to both complements so that, even with no drive signal, each complement remains fully on. Because they have the same amount of current running through them at all times, under duty and at rest, they draw as much power at idle as they do at full volume!
Class A/B is simply a combination of the two previous methods. Each complement draws current during the entire cycle, just drawing slightly less during its rest half of the cycle. This prevents it from ever switching completely off, thereby providing a much faster turn on response than a class B device when called upon to deliver its half of the output.
If you were to take a close look at the resultant output signal from each class of operation, you could see why no one uses pure class B amplifiers for audio applications. There is a marked distortion, right in the middle (vertically) of the reproduced audio signal, as the complement called upon for duty takes a fraction of a second to 'switch' on. The brief period of time required for turn on causes a gross distortion in the waveform. The result is very amusical. Class A/B is a much better method, as each transistor is always slightly on. This prevents 'hard' on and off switching, smoothing out the 'notch' distortion from class B operation quite considerably. Most of todays audio amplifiers operate in Class A/B. Finally, with class A operation, the devices are completely on all the time yielding the lowest switching distortion available from a Push-Pull design."
For completenesses sake, I'll add that single-ended amplifier designs (non-push-pull in other words, with only one - or one paralleled set - of output devices handling the entire waveform cycle full-time) are by definition always running in class-A mode of operation, the corollary of which is that class-A/B (and class-B) modes of operation apply only to non-single-ended (push-push or shared-duty-cycle) designs. Also that class-A/B designs, when running at low output powers, essentially operate as full class-A, the extent of which is determined by how much bias is applied to their output devices: the more bias employed, the higher in power the amp operates as class-A before merging into class-A/B as power increases (typically from just a watt or two up to several tens of watts in higher-biased designs). And a rule: the higher the bias setting (the more an amp is biased toward class-A), the more power the amp draws from the wall and dissipates as heat for equivalent rated output power (in other words the lower the amp's efficiency), so the greater the need for sufficient heat-sinking (in transistor amps) in order to keep the output devices operating within their safe temperature range (class-A runs hottest, being maximally efficient only at full output).
Hope this helps (and that I didn't f*** up my addendum!) - there's more on this subject in the archives as well.
