A diagonal is a line that connects polygon vertices in editable poly and Edit Poly objects. Its function is primarily to resolve the polygon into triangles at render time, especially if the polygon becomes non-planar via transformation of its vertices. Such transformation and certain other operations can, incidentally, cause automatic rearrangement of a polygon’s diagonals.

Diagonals on the default Cylinder primitive

Diagonals are normally invisible, but in 3ds Max they appear as dashed lines when you use the Turn or Edit Triangulation tool. Unlike edges, diagonals cannot be transformed, or acted upon with tools like Chamfer. This is different from the hidden edges in editable mesh/Edit Mesh objects, which are actual edges and can be made visible, transformed, and manipulated with any editing tool.