The Heston model lets volatility itself be random: the variance follows a mean-reverting square-root process that is correlated with the stock price. This simulator shows sample paths of price and variance, the effect of mean reversion speed, long-run variance, vol-of-vol and correlation, and prices a European option by Monte Carlo.
Market option prices imply different volatilities for different strikes (the volatility smile and skew). A random, correlated volatility produces fatter tails and skew, which a single constant volatility cannot.
A negative ρ makes volatility rise when the price falls, the typical equity pattern. It skews the return distribution to the left and steepens the implied volatility skew.