Explain Class A amp to non audiophile friends

A reasonable analogy could be:
The transistor is like a lit path. The music is like shadows moving down this path.
If the path is fully lit 100% of the time, then the only issue is the shadows moving, (music)
in an AB amp, the light AND the moving shadows are being constantly varied. So the shadows may be disturbed by the light (Transistor bias) flickering.

First you have to think about the waveform of a sound, it has a peak and a trough and it cycles from peak to trough over and over at a certain frequency.

With a Class A, the amplifing device is drawing more than enough current at all times throughout the whole cyle and is being called on to amplify the whole cycle from peak through trough. There can be one or more amplifying devices -- a tube, a transistor, etc.

With a Class B there has to be at least two amplifying devices per channel -- a pair of transistors or tubes (or two pair or three pair etc).

The signal is split going into the output devices so that one device is amplifying the peak of the waveform and one is amplifying the trough of the waveform. When one is working the other is switched off. This results in crossover distortion at the point when the devices switch.

In Class AB it's like Class B but the "resting" device isn't ever fully switched off. This reduces the crossover distortion.

Is the crossover distortion of class AB amplifiers actually audible?

Charles1dad, Yes it is. You have to keep in mind though that the ear hears many distortions as tonality issues. Also, the presence of distortion tends to obscure detail so in the range where the distortion appears the amp will likely sound harsher and less detailed.

In Class AB it's like Class B but the "resting" device isn't ever fully switched off. This reduces the crossover distortion.

The above statement is incorrect. If the device does not go into cutoff it is by definition a class A device. If it is class AB, the output tube or transistor will stop conducting during part of the waveform.

OK, here's an explanation for your non-audiophile friends & for you:
class-A amplifiers are a class of power amplifiers where the output transistors (or output stage) driving the loud speakers are always on & are always dissipating the maximum wattage that the power amplifier is rated for. Due to this fact, the heat sinks of class-A power amplifiers get very hot - 54C is considered the norm. Class-A power amplifiers actually run a bit cooler when the music is playing because a significant portion of the output wattage is delivered to the loudspeaker (rather than being dissipated as heat when no music is playing). The advantage of class-A power amplifiers is that, since the output stage is always on at full power, there is minimal amount of signal distortion (THD).

in a class-AB power amplifier, the output stage driving the louspeaker is biased at a very low level in comparison to a class-A power amp such that the output stage is considered to be weakly on (as compared to being full-power on in class-A and completely off in a class-B power amp). The reason for having the output stage weakly on is to avoid what is called as "cross-over distortion". Cross-over distortion occurs when the power amp needs to follow a music signal that is going from a positive cycle to a negative cycle or vice-versa and some time is required for the transistors servicing the negative cycle to turn on (pos cycle --> neg cycle). The advantage of a class-AB power amp is that it consumes much less power during idle & remains warm to the touch (as opposed to hot/scalding to the touch for a class-A power amp). The cross-over distortion is minimized in a class-AB power amp but I believe that it is not eliminated.

There are several well-known amp designers who subscribe to the view that a class-AB power amp can sound just as rewarding as a class-A power amp & that it is all in the implementation.

Hope that this helps.....