I'm going to say this very simply ignoring all intricacies....
Push - treat the film as higher ISO than rated on box
Pull - treat the film as lower ISO than rated on box
Stop - relative unit measure of exposure. 1 stop means twice as much or half as much
So say you have a film rated at ISO 400. If you put it in your camera and set your ISO dial to 800, you are PUSHing. Further, you are pushing by ONE stop because your aperture/shutter speed combination will provide half as much light to the film.
Also, say you have a film rated at ISO 400. If you set your camera to ISO 200, you are PULLing. Further, you are pulling it by ONE stop because your film will get exposed twice as much.
Because your film will be over/under exposed, most of the time, development time gets adjusted. Typically more or less 20 to 25%. This is done to get the density/darkness of the film about right.
It gets infinitely complex from here but that's pretty much the basics.