Principal curvatures are defined as follows: take a plane through the point that contains the normal and interesct it with the surface to get a curve. As you rotate the plane around you get different curves of varying curvature and the maximum and minimum values of this normal curvature are the principal curvatures. Take a look at Do Carmo's book entitled Differential Geometry of Curves and Surfaces. It's one of the best texts on this topic.