Volatility, as is normally understood in the financial markets and spoken of by the vast majority of traders, bankers, brokers, and other financial professionals, is of two kinds: historical volatility and implied volatility.

Volatility is a measure of fluctuations in an asset's price such as prices of stocks, stock indices, bonds, foreign currencies, commodities, etc. In statistical terms volatility is simply the standard deviation of a time series and that is exactly the way historical volatility is calculated for all assets. If you take a series of asset price, say over a period of one month or one year, and after having calculated the returns from these prices you take the standard deviation of those returns then you will get the percentage volatility of that asset over that time period. This is normally how historical volatility is quoted in the financial markets. For example if your broker says that the historical volatility of S&P 500 index is 15% over the last six months what he means is that the standard deviation of the returns of the S&P 500 index, calculated from the daily or weekly values (prices) of the index, over the last six months is 15%.

There is another kind of volatility that is not calculated but rather inferred from, or implied by, the option prices that trade in the markets. An option's price is amongst other things is a function of the volatility of the underlying asset on which the option is written. All things being equal if the volatility of the asset increase, thereby increasing the fluctuations in the asset price the price of the option will increase and vice versa. However, option prices are directly observable from the markets. All major assets, such as stock indices and stocks, bonds, currency and commodity futures, etc. have options on them that trade on the major exchanges in the world. Therefore they have a price that is observed daily and that price is determined by the demand and supply of the options as well as the view that the investors have on the direction of the underlying asset. Therefore, if we can observe the price every day we can infer from that price what is the volatility that has been factored into that price (by the traders, investors, speculators, etc.) However, to get a precise measure of that volatility we need some kind of a mathematical formula or equation into which if the price is input, holding other variables constant, we can get the value of the volatility. That formula is the celebrated Black-Scholes equation which, (or a variant of that formula) is universally used to estimate (infer) the volatility of assets by plugging in the observed price of the option as the input. This volatility that is implied by the option price of the asset is called the implied volatility of the asset. Implied volatility is common parlance amongst option traders in banks. Implied volatility is always quoted along with the time, i.e. 3 month implied volatility of S&P 500, 6 month implied volatility of Dollar-Yen, etc. The time shows the maturity of the options from which the implied volatility is estimated.

If the 3 month implied of volatility of S&P500 is 17%, it means that the volatility estimated from the observed 3 month S&P 500 futures options is 17% and this number could well be different from the historical volatility of the S&P 500 futures.