The simple explanation:

Basically think of a speaker as bucket and the amplifier as a well. The speaker places a demand on the amplifier. If the amplifier and speaker are both 8ohm nominal(average) and the speaker and amp never changed in their demands then everything is fine. We call that an easy load for the amplifier.

However amplifiers and speakers are not just their average. When the impedance of the speaker drops it requires a lot more amplifier power to keep the same volume level

Consider a speaker for example that might be 8ohms in the treble. If in the bass notes the speaker drops to 4ohms, the speaker will now request twice the power from the amplifier to achieve the same volume in the treble. So if in the treble the amplifier is putting out 5 watts and the bass passage comes along the speaker would have to put out 10 watts to hit the same volume level it was doing in the treble. And if the speaker drops to 2 ohms then it would request another doubling of power or 20 watts. for each halving of the ohms requires a doubling of the power. At 1 ohm it would request 40 watts.

So the term a benign load of a speaker rated at 8ohms to me would be a speaker that does not dip below 3ohms. Most amplifiers can get close to doubling their 8ohm rating. It is not completely necessary to get double. For instance if you have a 40 watt amplifier and you are listening to a 90db sensitive speaker at an average 90db (quite loud) then you are using 1 watt of power. If the speaker hits a bass line and drops to 4ohms then the amp will need to use 2 watts to meet the demand.

If however you are playing very loud say at 105db - you would be using 32 watts of your 40 watt amplifier. If in that bass passage it drops to 4 ohms the speaker is requesting double the 32 watts or 64 watts. The amp is only rated for 40 watts. Still if the amp is rated for 70 watts into 4ohms it will still meet the demand even if it can't quite double it's rated output. Further even if the speaker demanded say 75 or 80 watts - In short bursts amps can likely handle this but if it is prolonged the amplifier will go into clipping or distortion and will send a high powered distortion to your speaker which could damage the loudspeaker or the amplifier. (if the speaker dropped to 2ohms it would request 128watts and this would be well beyond the amplifier and it would clip and possibly blow the amplifier's on board fuse and shut off to protect the amp and your speakers).

As you can see if you play very very loud and the speaker dips down a lot in ohms (impedance) then you can see why people tend to like higher power amplifiers with not so easy to drive speakers.

Plus many makers play with the numbers - some amps may produce 100 watts at 1khz but not necessarily anything remotely close at other frequencies.

Some of the better amps actually don't double into lower frequencies. The Sugden A21a at 20 watts into 8ohms only muster about 11 watts at 4ohms. So it's a double whammy. When the speaker dips to 4ohms and wants twice the power the Sugden not only can't double the power it actually halves it's power. This is why it is a bit of an idiosyncratic amplifier and won't just work with any loudspeaker. SET amps typically do this and it is a major drawback when partnering with loudspeakers - they have to be relatively sensitive but more importantly the impedance has to not drop much (hence benign or stable impedance).

Why you might ask would someone want an A21a if it can't double it's rated output - because many people feel that the sound quality of the single ended class A (no feedback) sounds very much superior to the high current (double it's power) push pull amplifier designs.

Benefits

* Simplicity. An audio amplifier cannot be much simpler than a Class A single-ended.
* Overall low harmonic distortion with small signals. By nature Class A amplifiers do not suffer from crossover distortion.
* Small roaming of anode bias current does not do anything catastrophic.

Drawbacks

* Low efficiency. All Class A amplifiers consume power regardless of the signal amplitude.
* Second harmonic distortion at high signal level is a normal feature of single-ended amplifiers.
* Compared to the amplifier's low power the output transformer is heavy and expensive.

So when buying an amplifier you have to generally know the kind of speaker and at what level you intend to play. At low to moderate levels I have found that lowish powered Single ended amps have sound superior even with tough speaker loads and lowish sensitivity. However at louder levels these amps are not going to cut it. So do you listen louder more often or medium low levels more often.

With highish high and very high sensitive speakers that present an easy load they can be very comfortable with 2-30 watt amps depending. IME I have found lower watt amps tend to sound better and the systems using them have generally sounded better to me as well. But it also tends to cost more.

Some speaker makers do not provide the minimum impedance so generally it is safer to go with their minimum recommended power rating which kind of gives you a clue as to what will be powerful enough to still play loud. Both of my speakers can play to deafening levels with my 10 watt amp and I never get past the halfway point on either with very tightly controlled bass.