I understood ACF usefulness, with a temperature example... If we have a temperature time series, it is useful to know (for example) how correlated the temperature of past month is with this month.
But I do not get the logic behind PACF... PACF in my example would be, using July's temperature to predict September, given we know August's temperature.
What does it mean that we can "control" the other lags?
In Wikipedia it says
PACF contrasts with the autocorrelation function, which does not control for other lags
Unfortunately I cannot relate this to a real life example.