The picture you've provided includes the answer that you require, the water surface elevation is the elevation of the water as depicted on the upstream portion of the culvert.
Therefore, the headwater elevation above the culvert pipe is providing a certain amount of pressure head that is contributing to pushing water through the pipe (in addition to gravity and velocity).
To clarify, the situation depicted in that image is a pipe in a pressure flow situation (as opposed to an open channel flow situation). The Normal Water Surface Elevation is what calculations would indicate the surface elevation should be when the system is analyzed without considering the downstream impacts.
What's not depicted is what those downstream impacts are. For example, they could be a blockage or other constriction in the pipe or perhaps a tailwater elevation, which is when the elevation of the water surface at the point of discharge. Were the pipe to discharge partially or fully below the surface of a wet pond, that tailwater induces a back pressure on the system which affects the hydraulic grade line profile across the pipe network.
If you are dealing with a pipe network, it is extremely important to be cognizant about when and what causes your system to go into pressure flow conditions. Generally, though, if your observations or calculations indicate a headwater at some point, you've entered a pressure flow scenario for that pipe and it is very important to review the hydraulic grade line profile through the network to ensure you don't have water coming out of your inlets.