Recently I traveled to Europe (you may have heard) and there were a few situations where I pushed my film. By that I mean, instead of setting my camera to the speed (or ISO / ASA setting) of for example 800, I pushed it to 1600. Let me explain, ISO or film speed is the level of sensitivity or rating a film has. Works in a similar fashion to digital, except it's electronic with digital and chemical with film.
Cinestill 800t, is a perfect match for night time photography with lots of artificial, tungsten or fluorescent lighting. 800t is actually white balanced to tungsten light, whereas most other films are balanced to sun light.
Pushing the film from 800 to 1600 allowed me to shoot at a higher shutter speed, minimising (not completely) camera shake and producing blurry photos. The processing time of the film has to be adjusted to suit how many stops the film has been pushed. For example 100 speed film might get pushed from 100 to 800, which is 3 stops of exposure. 100, then 200 (1st), 400 (2nd) and then finally 800 being the 3rd stop. A stop is essentially an adjustment of exposure. Again, working in a similar fashion to digital.
*Please note that learning about the basics of ISO, shutter speed, aperture would give you a better understanding of the different stop instances.