Overview
A stochastic volatility model is one where the volatility, {% \sigma %} is not a constant. Typically, the square of the volatility is modeled as an Ito process itself.
Geometric Brownian Motion
The geometric brownian motion version of the process is probably the most common, because it is used heavily in finance. The price of an asset is modeled as the Ito process {% S_t %}.
{% dS_t = \mu_t S_t dt + \sqrt{V_t} S_t dW_1 %}
The square of the volatility is then also modeled an Ito process,
{% dV_t = \alpha(S_t, V_t, t)dt + \beta (S_t, V_t, t) \sqrt{V_t} dW_2 %}
{% \langle dW_1, dW_2 \rangle = \rho dt %}