This is an important topic among Car Audio and Home/Pro Audio people alike. Clipping is the term used when an Amplifier is overdriven. (Pushed too hard) This causes a sine wave seen here:

To look more like a square wave, seen here:

Why is this a bad thing? Well if you look at the peaks of the wave, they are much longer on a square wave. This means that the power the sub sees is not only greater, but the high power regions are much longer, creating MUCH more heat, not even considering that the signal is now "dirty".
Lets say you have a 500w RMS sub, and a amp that produces 500w RMs @ one ohm. When the one ohm load is placed on the amp, with a properly set gain, and a knowledgable user, clipping is minimal, resulting in a fairly clean signal. There may be a square wave here and there due to inconsistancies in the track being played, but a well built product that is properly rated, will have no problem dealing with it.
NOW:
You crank the gain up, YAY ITS LOUDER!
Until you reach the volume where the amp begins to clip......Then suddenly everything becomes the same volume, and sounds... bad. (At least to the knowing ear) Given the enclosure is not a bandpass (which can mute distortion) it can be audibly noticed.
Now why can clipping destroy speakers? Because the peak signal is held for an extended amount of time. If the signal exceeds the RMS rating of the woofer, it generates HEAT because the energy cant be turned into motion anymore... Heat kills.
I hope this helps some newer car audio members.
Josh