Stochastic volatility refers to the idea that the volatility of a financial asset, such as a stock or option, is not constant but instead changes over time in a random manner. This concept is important in finance because it helps to better model and predict the behavior of asset prices, which can fluctuate due to various market factors. In mathematical finance, models like the Heston model incorporate stochastic volatility to capture the dynamics of asset prices more accurately. By accounting for changing volatility, these models can improve pricing and risk management strategies for derivatives and other financial instruments.