Push processing means over-processing photographic film; in other words, leaving the film in the developer longer than what is necessary.

Why and How?

There are many reasons for wanting to push process film. For example, if you are out on a job, photographing a concert. If you only have ISO 800 film with you, and you don't want to use a flash, you decide you wish you had ISO 1600 film. What you could do, is to manually adjust the ISO value on your camera to 1600, and tell the shop where you'll have the processing done that you want it push processed by one stop. In general, this means that you'd leave the film in the developer double the time than is recommended.

Other reasons for push processing might be if you want to do creative things with your photographs, or if you are trying cross processing

Pull Processing?

Pull processing is the same as push processing, but the other way around, namely leaving it in the developer shorter than what is necessary. The same applies as for push processing, just vice-versa :)