Dot3 lighting is something you already know. It's just standard cosine lighting. But with pixel shaders I can do this per-pixel instead of per-vertex and then linear interpolating across the triangle. With pixel shaders you don't 'guess' what color should be at point x,y you compute which color should be there.
Something graphics programmers have wanted to do since the dawn of 3D. Compute lighting properties at the pixel level instead of the vertex level.