The code snippet given in the scrollable window depends on your choice of model and rendering method. In the case of Spline Only, the code shows the OpenGL functions required for OpenGL to generate the points used to display a curve (or at least an approximating curve). If the spline is composed of more than one curve, the code is repeated for each curve. The link "OpenGL Functions" takes you to the page that discusses each of the functions.
If the choice of model is Motion Path, the necessary code including the translation that moves a sphere along the spline is shown. In particular, the sphere moves from one point in the spline to the next (or previous). The coordinates of the points are computed using the formulae presented in the Discussion page versus through OpenGL function calls.
The code shown for the choice Extrusion in Z Direction is for creating a GL_QUAD_STRIP from the points in the spline and points above them at the distance height. As in the case of Motion Path, the points are computed versus provided by OpenGL.
Last, with the choice Surface of Revolution (about either available axes), the code snippet shows how to generate a sequaence of quad strips from the points in the spline. In particular, you should think of the surface as made up of bands around the axis of revolution with each band formed with a quad strip. Also, the top and bottom of each band is a circle with its center at the axis of revolution. In turn, we use polar coordinates to compute the points for each quad strip.