Kruger:

When I refer to underexposure in a push scenario I mean that you are treating the film as if it had a higher speed than it does. Push simply means overdevelopment. It doesn't decrease film speed. It actually helps maximize whatever speed the film has. What I meant is that this overdevelopment technique is often used when people want to try to use their film at a higher speed because there is not enough light. So for example, someone using an ISO 400 film might expose the film as if it were an 800 speed film (which means underexposing), and overdeveloping in an attempt to compensate for lost shadow detail. Exposing a 400 speed film at 800 and overdeveloping ("pushing") would be a 1 stop push.