GARCH, or Generalized AutoRegressive Conditional Heteroskedasticity is a generalization of the ARCH model. It is used to model the time-dependent conditional variance (volatility) of financial time series. A GARCH model represents the current volatility in terms of both past volatility and past errors. E.g. in the standard GARCH($q,p$) model we have $$\sigma_t^2 = \omega + \sum_{i=1}^q\alpha_i\varepsilon_{t-i}^2 + \sum_{j=1}^p\beta_j\sigma_{t-j}^2$$ where $\varepsilon_t$ is the error of the conditional mean model and $\sigma_t^2$ is its conditional variance.