Any magnet driven cone has a maximum throw (excursion)-- the max distance the woofer can be pusted outward. When it hits this point, it will often make an unpleasent noise (because it is trying to vibrate a full cycle to complete a wave- and insead it hits its max and clacks).
So, it just means the full travel of the driver has been exploited, and you are overdriving it.
When my Woofer (A Female Doberman Pinsher) Farts we usually vacate the room! (Quickly!)
If a Driver Bottoms out (the motor structure pulls the driver down past it's mechanical suspension travel) it will make a loud *CLACK* sound as the Voice Coil Former physicaly touches the T-Yoke (Magnet Backing Plate). This can cause the Voice Coil Former to bend or warp from the blunt force (The Former is usually Kapton or some sort of Pressed Paper Material) If the Voice Coil Former is bent then the voice coils will also be bent which can cause them to drag inside the Magnetic Gap and will ultimately lead to a short circuit as the Voice Coil repeatedly rubs against the Magnet and rubs the Shelacking off of the Voice Coil Wire and ultimately shorts out.
When the driver is overextended the opposite way (outwards) the Surround will often make a very loud *POP* sound as it is traveling further than it was designed to do. Over Extending the driver this was is slightly "safer" because the surround usually won't let the driver go any further. But if the surround is not strong enough to stop the force of the moving cone it can cause the surround to tear, or seperate from the cone (it would most likely tear first as the glue they use to bond a surround to a cone is fairly strong stuff). And if the Motor Structure is strong enough it is also possible to dislocate the whole Voice Coil/Former assembly from the underside of the cone.
Either way, Pushing a driver past it's linear suspension travel is BAD and if you hear that sound then it's time to quickly turn the volume down and figure out why it is that you care causing this to happen.
When an Amplifier clips it sends out square waves (imagine an ocean wave.. Nice and rounded crests.. Now lop off the top and you have a rounded slope with a flat top) Square waves will fry tweeters instantly if they do not have protection circuits (and still even with protection it could still fry it..)
Clipping the Amp it's self can ultimately lead to failure from just driving them amp too hard but it doesn't happen as "instantly" as speaker damage will.
If you are getting Popping sounds from a Mid Range or a Sub Woofer and the cone is moving a good deal, chances are you have too much power, rather than not enough.. When you tend to clip and amp is when the speaker can barely be driven with the amplifier at full gain (the speaker is hardly moving) but it's being sent a clipped signal because the amp is trying to work too hard.. The speaker tries to reproduce the square waves and will ultimately fail from heat damage to the voice coil..
The problem is as the article states, today even the cheapest of amplification units are far better dynamicaly then they were 10 20 years ago. Clipping is not easily heard by a novice or a pro when you have amps capeable of wide dynamic ranges from practicaly zero cycles clean up to 100 thousand cycles.
I stick by the rule that too much power is never bad but not enough power is a very bad thing. It's better to have way more head room than you will ever need, and run the gains low.. Then to have too little power, run gain full and cause the amp to be overdriven and start sending out clipped signals...
Some tweeters are a little more "stable" with square waves than others, Ribbons can handle somewhat square waves but Dome's can't do it they just give up the ghost in no time.
When the day comes that a speaker can faithfully reproduce a Square Wave, that is the day that all of this clipping talk becomes a thing of the past.
Ohh don't even go there... California is the reason the company I work for is on the verge of Bankrupcy! (I work for a Power company and Cali screwed us big time!)