Michromatic's Mark Ryan Sallee helps simplify it all in this easy to follow video, in which he covers how sensor sizes crop images and change the focal length and angle of view of lenses, as well as, yes, a little bit of math that you might want to hang on to.
Crop factor is for understanding how the field of view of a given focal length is going to change as you move from camera system to camera system.
Understanding crop factor won't necessarily keep you from being able to make films like, say, not knowing how to hit the record button would, but it certainly will save you many headaches -- and money! It's a good idea to educate yourself on what the difference is between different sized image sensors, other than price of course, before you invest in lenses and a camera with a sensor that produces images that you weren't expecting.
And look! Now that you understand crop factor a whole lot better, you can participate in all of the arguments raging on the internet about full frame vs. Micro 4/3 vs. every other type of sensor that exists in the natural world. Delightful! Be safe and have fun.