Normals are vectors which point straight out of the surface they are attatched to and cannot really be drawn with points. If you try to they will all appear in a sphere around the origin, as normals are always of length one (or ought to be), and in a complex mesh normals will be pointing in more or less all directions. If you want to render normals on your vertices I'd suggest drawing GL_LINES from the vertex to a point at vertex + normal.

The standard graphical use for normals is lighting. Look up tutorials on this if you're not sure what to do.