How Is Implied Volatility (IV) Derived from the Market Price of an Option?

Implied volatility (IV) is derived by taking the current market price of an option and using it as an input into an option pricing model, like Black-Scholes. The model is then solved backwards for the volatility input that makes the model's theoretical price equal to the market price.

It is the market's expectation of the underlying asset's volatility over the life of the option. IV is not directly observed but is an inferred variable.