Generally I look at these plots to see which lag(s) have the highest correlation coefficients to help determine differencing order for the AR component and seasonal interval if I'm contemplating some sort of seasonal ARIMA model. I also try to use some process knowledge to validate, in a non-statistical sense, my differencing and seasonal interval guesses. For example...if I were monitoring temperature in my home, controlled by a thermostat, on a minute by minute basis, I'd suspect a differencing order close to 1 to be the best. If I were monitoring my home's monthly natural gas consumption, I'm guessing that a seasonal lag component would be 12 months out in time. Seriesg.jmp in the JMP Sample Data Directory is a good sample data set to illustrate these concepts.
