Meshes All objects in Blender are meshes, which are made of points, vertices, edges and faces.
Point The origin point describes the location of the object.

The orange dot represents the origin point. The shape of the object is built around this point.
Vertex A vertex point is just a point. A mesh is made up of a series of these points.

To create a new vertex point, in Edit mode select an existing vertex point then press Ctrl+LMB.
Edge Edges connect vertices together.

An edge connects two vertices by a straight line. Think of edges as wires that you can see when you look at a mesh in wireframe view. They are usually invisible on the rendered image. They are used to construct faces. To create an edge from two selected vertices press F.
Face A face is made when edges and vertices combine together to form a solid surface.

A face is defined as the area between either three (triangles) or four (quadrangles) vertices, with an edge on every side. Triangles are always flat and therefore easy to calculate. On the other hand, quadrangles deform well and are therefore preferred for subdivision modeling.

To create a face, select three or four suitable vertices and press F.