Quote from nonprophet:
GARCH has much to do with complex math and nobel prizes, but absolutely nothing, zero, zippo, nada, nix, null with trading or making money.
Without descending into theoretical debate, your statement is simply false. Had you said "Having nice closed-form solutions has little to do with trading or making money", then I would have agreed with you. There are numerous applications of GARCH that are in wide use by practitioners, including but not limited to (generally) GARCH as a component of VAR analysis, and GARCH as a component of option pricing. That being said, "the model is only as good as the mathematician". One cannot blindly apply GARCH or any other model without the required fundamental and theoretical background. In that sense, I agree that GARCH is of "zero use" to a "seat of the pants trader".
As to the initial poster's question, GARCH and other volatility models cannot be neatly summarized in a paragraph or two on a public message board. You need to develop a fundamental and theoretical background to in order to understand, evaluate, and apply these models in practice. Otherwise, you are wasting your time. For a "seat of the pants" starting point, see the following links:
http://en.wikipedia.org/wiki/Volatility
http://en.wikipedia.org/wiki/Stochastic_volatility
-segv