the math behind it is pretty complex. i'm a math major going into my senior year of undergrad, and i don't understand a word of that wikipedia article.
it's a result from a branch of math called topology, which deals with surfaces and maps between them in different dimensions. pretty cool, but it requires a lot of background (that i don't have) to really grasp.
the videos are just a way to visualize the result. proving it is much more difficult, i would imagine.