Generalised AutoRegressive Conditional Heteroscedasticity

An autoregressive process is one where there is a non-zero correlation between past events and future events
Heteroscedasticity refers to changing variance
These are models that allow variance (or volatility) to not be constant

Empirical studies have suggested that quiet periods of low volatility tend to be interspersed with clusters of high volatility
This implies that volatility itself is dependend on past volatility
Which implies that volatility is not completely random but is conditional on past events