The normal map posted above specifies the direction of each "3d" normal vector per pixel. Taken from the normal map, all normals have the same length. How light each pixel appears is calculated from the angle between the normal and the light source. If the light shines directly on the normal (both vectors are exactly opposite), the pixel is lightened 100% of the light's light. If the angle is 90°, the pixel is lightened 0% from the light. Normally, a diffuse light source (which lightens all pixels the same, regardless of their normal vectors direction) is added too. The smooth ending of the light radius is achieved by making the light loose it's strength the further away it is from the light source (normally quadratic).