Basically clipping occurs when the relevant section of an amp runs out of voltage or current,and the top of the music waveform is quite literally clipped...this results in large levels of high frequency harmonics being produced,as the waveform now approximates a square wave.
It's the high level of high frequency harmonics that damages your speakers,and usually it's the tweeters that get damaged.
It's most likely to happen when a relatively low powered amp is driven hard into inefficient speakers,so if the amp/speaker match is sensible,then clipping should be unlikely at most levels.
if it does begin to occur,it's generally obvious as a gradual hardening of the sound as the amp begins to run out of grunt,followed by a pretty awful deterioration once the clipping point is reached.