Volatility is a measure of the relative rate at which the price of a security or contract fluctuates. It is defined as the annualized standard deviation of daily change in price or, in other words, the square root of the security's annualized variance.
A volatile market, contract or security is one whose price tends to fluctuate sharply and regularly.
One measure of the relative volatility of a particular stock to the market is its beta. A beta approximates the overall volatility of a security's returns against the returns of a relevant benchmark such as the S&P 500.
Volatility can be used in various manners to measure market activity. Traders use measures of options volatility to make decisions about changes in market direction. For example, a rise in the implied volatility of options of strike prices below an underlying security's price (also known as "downside puts"), this may indicate a heightened concern of an impending decline in the security's price.
The VIX is a volatility index developed by the Chicago Board Options Exchange in 1993 to measure investor sentiment and market volatility. It is often referred to as a "fear guage," because it tends to move inversely with the direction of the stock market.