A hyperextension is very similar to the back extension, except you perform hyperextension.  In a normal back extension, you will want to stop once your entire body is perfectly straight.  With hyperextension, you bring your back past parallel so that your body makes a subtle "V" shape. Very subtle.  When performing these, do not bend so far that your back begins to bend and form a "U".  The "hyper" part is small but that little bit of extra flexion creates much higher activation.