"Many economists maintain that money neutrality is a good approximation for how the economy behaves over long periods of time but that in the short run monetary-disequilibrium theory applies, such that money would affect output."
It is an important idea in classical economics and is related to the classical dichotomy. Money neutrality holds that the central bank does not affect the real economy (e.g., the number of jobs, the size of real GDP, the amount of real investment) by printing money. Any increase in the supply of money would be offset by an equal rise in prices and wages.
Superneutrality of money is a stronger property than neutrality of money. It holds that not only that the economy is neutral as to the level of the money supply but also that the rate of money supply growth has no effect on real variables.
In this case, both the money supply and its growth rate can affect nominal variables such as the price level and inflation rate in the short run.