What is a Grid Convergence Angle?

Answer

The Calculate Convergence Angle tool calculates the angle between the Central Meridian of the projected coordinate system applied to the data, and the line which intersects the point and runs from the point to the North (or South) Pole.  A Convergence Angle between the Central Meridian of UTM Zone 15 North and the USGS Survey Control Point Meade's Ranch is shown in the following illustration.

Note: 
Convergence angles cannot exist in a Geographic Coordinate System, or in some projected coordinate systems like Web Mercator, because in these coordinate systems ALL lines of Longitude point directly at the North Pole.