It's when you push a speaker to the point where it can't accurately produce the sound, so you start hearing the byproducts of the speaker straining to try. Usually happens when you run too much wattage through it (i.e. a 75 watt head through a 30 watt speaker), and most people consider it to sound very nasty. Plus it's damaging the speaker...
It's distortion of the signal due to pushing a speaker hard, like josephde explained. Some people hate it. It's essential to some guitarist's tone (see Derek Trucks).
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