Explaining the GARCH(1,1) volatility model

Explain in plain language what a GARCH(1,1) model does, then write down its equations and say what each parameter represents.

Variance today is a weighted mix of a long-run level, yesterday's squared shock and yesterday's variance. With $r_t=\mu+\epsilon_t$, $\epsilon_t=\sigma_t z_t$, the model is $\sigma_t^2=\omega+\alpha\epsilon_{t-1}^2+\beta\sigma_{t-1}^2$: $\omega>0$ sets the floor, $\alpha$ is the reaction to news, $\beta$ is persistence. With $\alpha+\beta<1$ volatility mean-reverts to $\omega/(1-\alpha-\beta)$, reproducing volatility clustering.