Hello, I do not have a geometric background, but I have a research project requires me to calculate distances between, say, a conflict site and the nearest major city (with population more than 1000000). I wonder are there any good sources can help me understand how to calculate this distance and how this is done by ArcGIS (explain the formula used to calculate the distance in a simple way). Besides, are there any good source for illustrating how grid and centroid points are generated (and the math) in ArcGIS?

Thanks!

This is a surprisingly complicated question. The short answer is that ArcGIS can calculate distances in several different ways depending on things like which tool you use and which projection (if any) your dataset(s) are in, and it will calculate the distance how you tell it to do so.

As a starting point, here is a blog post comparing geodesic to euclidean distances (both of which can be computed in ArcGIS), but there are many, many resources out there devoted to this topic.

Also, see this link, which will you start you on your journey through the help pages:

How proximity tools calculate distance—Help | ArcGIS for Desktop