what is meant by the term normal to the surface
In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word normal is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. That is, any vector orthogonal to all in-plane vectors is by definition a surface normal. If a (possibly non-flat) surface S is parameterized by a system of curvilinear coordinates x (s, t), with s and t real variables, then a normal is given by the cross product of the partial derivatives.