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GARCH processes are used to model the conditional volatility of financial returns in discrete time. There are many many different types of GARCH, the most popular and simplest being the GARCH(1,1), where returns have mean mu and conditional variance vt (t indexes time): returnt = mu + sqrt(vt)et where et is a standardized innovation.
Conditional variance follows a first order autoregressive process: vt= a + b* vt-1 + c* vt-1*et-1^2
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A GARCH model is employed to help predict volatility (i.e. of stocks, XE rates etc) based on historical values through model fitting. Recent data is given more significance than older data. Compare to the least squares approach, which weights all the data equally. Since volatility is not the same across the entire data set (periods of volatility cluster together), this assumption is not valid. The related link provides greater detail and an Excel spreadsheet
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