Volatility refers to the degree of variation or fluctuation in the price of an underlying asset. In options trading, volatility is a crucial factor that affects the price of an option. When an asset is highly volatile, it tends to have larger price swings, and as a result, the price of an option based on that asset is likely to be higher. On the other hand, if an asset is less volatile, the price of an option based on that asset is likely to be lower.

Volatility can be measured in several ways, but the most common measure used in options trading is implied volatility. Implied volatility is a measure of the market’s expectation of how volatile an underlying asset will be in the future. It is calculated using the current market price of an option and other variables, such as the underlying asset price, strike price, time to expiration, and interest rates.

Options traders use volatility to assess the risk of an option and to determine the appropriate price for an option. Higher volatility increases the risk of an option, which in turn increases its price. Lower volatility reduces the risk of an option, which reduces its price.

Option pricing models require the trader to enter future volatility during the life of the option. Naturally, option traders don't really know what it will be and have to guess by working the pricing model "backwards". After all, the trader already knows the price at which the option is trading and can examine other variables including interest rates, dividends, and time left with a bit of research. As a result, the only missing number will be future volatility, which can be estimated from other inputs These inputs form the core of implied volatility, a key measure used by option traders. It is called implied volatility (IV) because it allows traders to determine what they think future volatility is likely to be. Traders use IV to gauge if options are cheap or expensive. You may hear option traders say that premium levels are high or that premium levels are low. What they really mean is that the current IV is high or low. Once understood, the trader can determine when it is a good time to buy options - because premiums are cheap - and when it is a good time to sell options - because they are expensive.

In summary, volatility refers to the degree of variation in the price of an underlying asset, and it is a crucial factor that affects the price of an option. Implied volatility is a measure of the market’s expectation of future volatility, and options traders use volatility to assess risk and determine the appropriate price for an option.