Clipping is what occurs when an amplifier reaches it's electrical limits. All amplifiers are a sum of their parts. The weakest part determines it's limitation of output. If an amplifier is rated to deliver 5 watts RMS and 10 watts Peak and you take it past that point the amplifier will begin to clip audibly and the sound from your speakers will become distorted. Most commonly clipping sounds like light popping, crackling, static, or garbled noise that accompanies the original source program (music, movie soundtrack). This sound is undesirable for your ears as well as the high frequency drivers of the speaker (tweeters, midrange) most specifically which ever driver operates closest to the upper mid band and lower high band (1000 Hz on up to say 6000 Hz, someone correct me if I'm wrong).
Not only is this a hazard to the sensitive drivers of the speaker, but it is also dangerous for the amplifier. A transistor (an output device) that is driven to its maximum capacity will get hot, hotter than a stable tempurature and could cause it to fail.
I'll use this video of some Foreign folks overclocking a processor (basically a integrated circuit full of transistors) and then proceeding to remove the heatsink.
http://video.google.com/videoplay?docid=5393904704265757054#
Like the processor high output transistors (those used for final amplification) require adequate heatsinking in order to dissapate heat which reduces resistance. If the transistor is not capable enough or the heatsink is too small the amplifier will clip easier.
Other forms of clipping can occur when the power supply is too small or the storage capacitance is inadequate for the task (what is adequate can change depending on the speakers being used).