Aggregate demand expansion = Inflation
Aggregate supply contraction = inflation
The first kind of inflation changes NGDP, while the second has minimal impact. This way, when we are in a recession and demand more inflation, what we really mean is that we need more of the first kind of inflation because we need more NGDP. If we were in the second situation, we wouldn't be demanding more or less NGDP because the supply shock would have had minimal impact.
Another example in which NGDP makes explanations easier is in discussions of whether deflation is bad in an economy. Often times, liberal economists will point to the recent recession and say deflation is bad, while libertarians might point to the late 19th century, early 20th century and say that deflation is good. The more correct answer is that stable NGDP is best. So because the first kind of deflation reduced NGDP, it was bad, while the second type of deflation kept NGDP steady, and therefore was good.
While NGDP is simple, it makes it hard to statistically show NGDP boosts RGDP. You can't look at a graph and point to any correlation; a skeptic could just say that it's the RGDP that's driving the movements in NGDP, and not the other way around. In the end, to explain the relationship between nominal and real output in AD shocks, I have to find specific channels, such as nominal debt. On the other hand, inflation and output make much more sense in terms of trying to find statistical relationships. These concepts are far enough in people's minds that a relationship doesn't seem like a tautology. However, when you start directly talking about NGDP and RGDP, it's too easy for people to think the observed relationship between NGDP and RGDP is just because the second is a component of the first.