Vertex Normal
Vertex normals are just like other normals - a 1 unit length perpendicular, but since points in space can't have perpendicular line - it has sense only when drawing a face.
How do vertex normals work
Both images are THE SAME 2 triangles from slightly different points of view.
Both images can be done with 6 pixels (the green and red one has same position in space, but different normals).
Left image: since the red and green normals are different - you can distinctly see how the color rapidly change from light green to darker one, but on the right image I have "merged" red and green normals (averaged them), therefore now you can't see the crease and the color changes smoothly - the normals are interpolated and create a smooth surface.