Paraphasing the better explanation:
the ability to play music at a moderately loud level without the distortion and compression you would hear when using a lower powered amp that is "clipping". Its about your amp being able to handle the demanding peaks and keep control during complex passagesIdeally the available dynamic headroom should be in the neighborhood of 20dB, a power multiplication factor of 100 times. So if you're running at only 2 watts per ch. average power, then you need a 200 w/ch amp to have 20dB of headroom & stay out of clipping. You don't use all of that amplifier power continuously, but you do need the large power reserves.