It stands for local volatility; in the context of option pricing, it is a type of volatility that locally (for a given function) depends on time and the value of the underlying asset. It is based on a model that is a generalized version of the Black-Scholes model. Though this model assumes volatility to be constant, local volatility is, to an extent, premised on the notion that volatility is not, and cannot be, constant (though the model of local volatility is static and is not designed to capture volatility dynamics withe the passage of time). This measure of volatility describes how the volatility of an option’s underlying asset changes in reaction to both its current price and with the passage of time.

Local volatility is particularly instrumental to pricing exotic options that cannot be handled under standard models. It is typically used to determine the value  of all combinations of strike prices and expirations (contrary to implied volatility that accounts for a single expiration ).