"Region" seems to be a very important concept in Mathematica's latest version. Where can one
find the more thorough introductory details about the concept of
Region instead of just the shattering examples in the document?
I think this question is broad since Regions are used in various fields for various purposes. Think computational geometry (Voronoi diagrams, Delaunay triangulations, Convex hull etc.), finite element methods (PDEs), solid geometry etc. In addition to the links provided by Mr.Wizard, here are some additional links that might get you started: