I have searched the ESRI kriging-related documentation but cannot seem to find relevant information on this. It's rather straightforward with the prediction feature from the geostatistical analysis extention to predict an areal-level value from a continuous surface interplated from kriging (e.g. ordinary kriging). But what are the maths behind this process? Is it some sort of moving average based on continous values for each areal unit? How is the average calculated? I only find the basic formula for point-location predicted values, but not for areal level values. Any help or pointers in this regard is greatly appreciated.

This process is conditionally simulating many point values in each of the polygons, then it's calculating statistics on these simulated points within each polygon.