ARIMA stablity

It is said you should check for the stability of the parameters. I don't know what they mean, its not significance and I don't think its Stationarity.
I don't have a really good quote (just a single sentence with no context). I will look for one.

A econometrist I read says differencing is not the way to go with ARIMA. Do you know what demeaning a time series is?