In stochastic volatility models, the variance $v_t$ is a random process of its own, driven by a second Brownian motion correlated with the spot:

\[dS_t = (r - q)\,S_t\,dt + \sqrt{v_t}\,S_t\,dW^S_t\] \[dv_t = \alpha(v_t, t)\,dt + \beta(v_t, t)\,dW^v_t, \qquad d\langle W^S, W^v \rangle_t = \rho\,dt\]

Heston is the case $\alpha = \kappa(\theta - v_t)$ and $\beta = \xi\sqrt{v_t}$.

Compared with local vol, which flattens the smile going forward, stochastic vol better reflects the forward skew (the smile implied at future dates).