Manual/Mesh Structures
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Mesh Structures: Vertices, Edges and Faces
In basic meshes, everything is built from three basic structures: Vertices, Edges and Faces. (We're not talking about Curves, NURBS, and so forth here.) But there is no need to be disappointed: This simplicity still provides us with a wealth of possibilities that will be the foundation for all our models.
Vertices
A vertex is primarily a single point or position in 3D space. It is usually invisible in rendering and in ObjectMode. Don't mistake the center point of an object for a vertex. It looks similar, but it's bigger and you can't select it. (Vertex example) shows the center point labeled as "A". "B" and "C" are vertices.
To create a new vertex, change to Edit mode, hold down CTRL, and click with the LMB 
.
Of course, as a computer screen is two-dimensional, Blender can't
determine all three vertex coordinates from one mouse click, so the new
vertex is placed at the depth of the 3D cursor 'into' the screen. Any
vertices selected previously are automatically connected to the new one
with an edge. Vertex labeled "C" is a new vertex added to the cube with a new edge (B to C)
Edges
An edge always connects two vertices with a straight line. The edges are the 'wires' you see when you look at a mesh in wireframe view. They are usually invisible on the rendered image. They are used to construct faces. Create an edge by selecting two vertices and pressing F.
Faces
A Face is the highest level structure in a mesh. Faces are used to build the actual surface of the object. They are what you see when you render the mesh. A Face is defined as the area between either three (triangles) or four vertices (quads), with an Edge on every side. Triangles always work well, because they are always flat and easy to calculate.
Take care when using four-sided faces (quads), because internally they are simply divided into two triangles each. Four-sided faces only work well if the Face is pretty much flat (all points lie within one imaginary plane) and convex (the angle at no corner is greater than or equal to 180 degrees). This is the case with the faces of a cube, for example. That's why you can't see any diagonals in its wireframe model, because they would divide each square face into two triangles.
While you could build a cube with triangular faces, it would just look more confusing in Edit mode. An area between three or four vertices, outlined by Edges, doesn't have to be a face. If this area does not contain a face, it will simply be transparent or non-existent in the rendered image. To create a face, select three or four suitable vertices and press F.
TODO:
Mesh Structures: Edge Loops and Face Loops
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