One of the things the National Emergencies Act does is require the president declaring a national emergency to say what powers are being activated. For the one you linked, you can see that in the original by looking up Proclamation 7463. I was able to find an analysis of the sections cited, in this doc: http://fas.org/irp/crs/RS21017.pdf
For this particular national emergency, they all have to do with special powers of the President to control how the military is staffed, call up reservists, change terms of duty, active duty status, things like that.
