What is Heston model?

The Heston model takes the variance to be a square-root process (One Quant Book 4, chapter 4):

with five parameters: the initial variance $v_0$, the mean-reversion speed $\kappa$, the long-run variance $\bar v$, the volatility of volatility $\eta$ and the correlation $\rho$. The variance stays non-negative and never reaches zero when the Feller condition $2\kappa\bar v\ge\eta^2$ holds.