What Is Implied Volatility?
Implied volatility, as its name suggests, is the volatility implied (contained or priced in) the price of an option. According to commonly used option pricing models (such as the Black-Scholes model), option prices depend on a number of factors, including among other things underlying price, time to expiration, and volatility. Other factors being equal, the higher implied volatility, the higher the price of the option.
The relationship between an option's price and volatility is measured by vega, one of the so called option Greeks. Vega is the first derivative of an option's price with respect to volatility.
Calculating Implied Volatility
Because the option pricing models are usually mathematically quite complicated (they reflect the fact that the exact relationship between volatility and option prices is also quite complicated), it is not possible to derive a direct formula for implied volatility from common option pricing models. However, you can get to implied volatility by trial and error, which is easy to do in Excel using the Goal Seek feature. The process is explained here: Calculating Implied Volatility in Excel
The easiest way to calculate implied volatility is using the Implied Volatility Calculator. Its user guide includes detailed explanation of implied volatility and its relationship with option prices. You can also use the calculator to model effects of volatility on option prices and individual Greeks.
You can also calculate implied volatility in the Black-Scholes Calculator using the Goal Seek feature in Excel.