Distortion in and of itself does not damage speakers. Here is an example (or a few). Let us say we have a speaker that handles 100 watts of continuous power. When an amplifier fully clips (distorts) it will double it's maximum continuous unclipped power (less than 1% thd). If we use a 50 watt amplifier on this speaker, fully clipped (distorted), it will NOT blow. The speaker's voice coil will NOT fail because we have NOT EXCEEDED it's thermal power handling. The only possible chance for failure here could be possible suspension damage due to odd order harmonic information.
Now if we had a 100 watt continuous unclipped amplifier on our 100 watt speaker and we fully clip it. We would now be sending 200 watts of power to our 100 watt speaker. Seeing as though our speaker can only thermally dissapate 100 watts of continuous power, the voice coil will surely fail (if left for too long), we will see a mechanical failure, or both. It is not recommended to exceed the speaker's continuous power handling capabilities. If a speaker only handles 120 watts continuous, use a 120 watt continuous amplifier, and try not to over drive it (the amplifier). Chances are you won't overdrive it as it will get very loud without distortion. The 120 watts will be plenty of power for extracting all the dynamics you need and the speaker will offer. If a speaker needed more power to get the most out of it, the manufacturer would rate it accordingly.
If we had a 200 watt continuous unclipped amplifier on our 100 watt speaker, and the amplifier was at full continuous output power, the speaker would fail thermally and /or mechanically as well, as we have exceeded the amount power that the speaker can safely dissapate. This speaker would fail even though no real large amount of distortion (probably below 0.07%)was present.
Back to the topic at hand. The amplifier would be the only piece supplying "dynamic headroom." What is "dynamic headroom?" It is extra, clean, unclipped power supplied by the amplifier above and beyond the continuous unclipped output level. Say you are listening to music and at a normal volume and all of the sudden there is a thunderous kick drum stike, or a hard rim shot on the snare. Those dynamics in the music require additional power from the amplifier to make them stick out the way they are supposed to. Having "dynamic headroom" available from the amplifier will make them sound more realistic. If an amplifier is starting to stress already (near its clipping threshhold) at the normal consistent volume and that same dynamic passage comes about, they (dynamics) may not stick out, sound realistic, or worse, distort. most good amplifiers will have around 3db of dynamic headroom. This can be hard to measure as there is no standard for measurement. Thus, it is NOT a good way to shop for amplifiers.
A speaker can be limited by how much dynamic capability it is capable of as well. If a person is already running a speaker at around it's continuous power level (which is usually VERY loud), and a person has an amplifier capable of produing more clean power, when the dynamic passage comes along and throws even more power at the speaker, (which is at the power handling limit) it will not really get any louder for the passage. It has reached it's full, safe dynamic output capability. This is called power compression. Say we have our 100 watt speaker from above, and we are running it at 100 watts continuous with a 150 watt continuous unclipped amplifier. Since we have a lot of dynamic headroom available in our amp, but are already at the thermal limits of our speaker, any extra power applied at this point really just gets wasted as added heat on the speaker's voice coil (power compression). Rather than adding additional dynamics, we push our speaker closer towards a thermal failure. If this continues over enough time, and heat continues to build, the speaker's coil will fail.
Edit:Sorry for the book.
