Here’s a Wikipedia article that describes a Brep, our Boundary Representation.
Boundary representation - Wikipedia
Some people find this diagram helpful.
http://developer.rhino3d.com/guides/cpp/brep_data_structure
Modifying the vertices of Brep isn’t going to help you. If you want to modify the shape of a surface, then editing the locations of a surface’s control points is one such way.
I see you’ve found the article in setting up a cage edit. Have you used Rhino’s CageEdit feature? Is this what you want to do?
I should add that cage editing is something you cannot do yet in RhinoCommon. But its on the to-do list for Rhino 6.