NURBS surfaces are mathematically calculated using parametric equations and a set of control points ordered into a patch. NURBS surfaces are able to be dynamically tessellated, unlike polygons. This gives them certain advantages since they offer precise surface information at any point on the surface.
The degree of NURBS curves indicates the highest power of the polynomial equation used to generate it. For example, a curve with degree 1 will basically use linear interpolation between the control points, ie, it will generate straight lines between all control points. Normally we use cubic curves since they give us curve continuity and are computationally cheaper than higher degree curves.