So many points of view .... Here's mine : )
For an amplifier or "gain stage" ( any form of amplification, be it in a preamp, phono preamp, etc..) to remain "linear" or "clean", it would amplify all incoming signals equally. The input and output waveforms would look identical with the only difference being "amplitude" or "volume" i.e. the signal goes in "weak" and comes out "strong" but looks like a mirror image with the same overall shape and duration.
If an input signal requires more gain than the amplifier can deliver, the peaks of the signal are distorted or clipped off (depending on the severity of power limitations ). This type of distortion can occur due to saturation of either the active devices such as the transistors, tubes, mosfets, etc... found in the driver or output stages OR the power supply being taxed beyond its' capabilities. Think of it as running a cars' motor well beyond redline ( saturation or "overload" ) or a cars' motor that is drinking fuel faster than the fuel pump could supply it ( starvation ).
Once "clipping" occurs, distortion of all types start to take off. Harmonics ( odd and even multiples of the main frequency ) are the primary "culprit", but other forms are also generated. This means that a 100 Hz signal that was "clipped" would produce notes at 200 Hz, 300 Hz, 400 Hz, etc... all the way up into the high treble region and beyond. Some amps, like tubes, will reproduce more even harmonics ( 100 hz x 2, 100 hz x 4, etc..) whereas most transistor amps will reproduce more odd harmonics ( 100 hz x 3, 100 hz x 5, etc...). Many integrated circuits ( IC's) tend to reproduce ALL of the harmonics. These are generalizations at best, but i hope that you can follow along.
Most people feel that even order harmonics ( x 2, x 4, etc..) like a tube clips tend to sound more natural and less harsh than odd order ( solid state ) harmonics. Since many IC's reproduce ALL the harmonics, many people say that everything is "COMPLETELY smeared" when they are used in circuitry. Quite honestly, I will agree that all of these things sound "different". Even amps using very similar parts can sound different due to various circuit designs, bias levels, etc... Each type of device has different strengths and weaknesses and that's why we have SO many different designs out there.
Since harmonics ( even, odd or all of them ) are reproduced ON TOP of and along with the musical signal that is already present, the upper frequency ranges are now seeing WAY more power than what they would normally see. On top of this, severe clipping results in increased duration of the notes, i.e. "hard / extended smearing", etc... Mids and tweeters now have to handle a greater percentage of power AND do it for a longer duration of time. As such, their smaller motors ( voice coil assemblies and magnet structure ) might not be able to dissipate near as much energy ( primarily heat ) as a woofer could. The result is a burned winding ( resulting in either a "short" or "open" in the voice coil), a deformed voice coil former that drags or rubs, a broken "flex lead", etc.. Woofers are rarely damaged when amps clip due to their sturdier motors and increased capacity for heat distribution. However, it is possible to damage a woofer if the amplifier is "passing D.C." (direct current) or it is not "built like a tank". If there is a lot of DC voltage present for an extended period of time, the woofer can even "flame out".
Besides the harmonics that are generated from pushing an amplifier stage too hard, I.M.D. (InterModulation Distortion) usually skyrockets also. What IMD does is to take and mix the signals ( both music and harmonics ) and creates even more chaos. Whereas you might have had a signal at 125 hz and 200 hz, you will now have signals that are the sum (125 + 200 = 325 hz) and the difference (200 - 125 = 75 hz). Add all of these multiples and divisions ON TOP of the energy already being reproduced by the harmonics and "regular music" being passed through the system and you have a real "energy mess" that the speakers are trying to deal with and dissipate.
Needless to say, music sounds "better" and "cleaner" when the gain stages are "coasting" and not being pushed. Speakers and amplifiers also typicall last longer if not "pile driven into clipping". Just like anything else in life, the more that you abuse it, the more likely it is to fall short of your expectations in reliability.
Something that is similar to overdriving amplifiers and clipping taking place occurs in speakers. This is called "compression", but is a WHOLE 'nother ball o wax. Somebody else can fill you guys in on that. I'm too tired tonight... : )
In the meantime, i hope this helps... Sean