What does it mean when they say ‘Volatility reverts to the mean?’

A: What it basically means is that extreme volatility–high or low–doesn’t last forever, and that a market will resolve itself one way or the other to return to its average historical volatility level, i.e., very low-volatility periods are generally followed by very high volatility-periods, and vice-versa. If you averaged these low and high volatility periods, you would get a value close to the average (the “mean”) volatility in a market calculated over a fairly long historical time period (say, 100 days).