A (Event generation) What information do you get...

The Meaning on that statement is that the total number of events is normalized to the calculated NNLO inclusive cross section.

The production itself is done at a lower order (LO or NLO), so the shapes of all the distrubutions reflect these lower orders.

But the total normalization is accurate to NNLO.

 

The total number of events are normalised by [itex]\frac{\sigma_{NNLO}}{\sigma_{LO/NLO}}[/itex]

 

So practically:

[itex] \sigma_{nnlo}/\sigma_{nlo} d \sigma_{nlo} /dX [/itex]

Where X is the observable. Practically though, POWHEG samples are not actually NLO accurate for distributions, since it's NLO+PS (not fixed order).