support vector machines - a simple explanation?

So, i'm trying to understand how the SVM algorithm works but i just cannot figure out how you transform some datasets in points of n-dimensional plane that would have a mathematical meaning in order to separate the points through a hyperplane and clasify them.

There's an example here, they are trying to clasify pictures of tigers and elephants, they say "We digitize them into 100x100 pixel images, so we have x in n-dimensional plane, where n=10,000", but my question is how do they transform the matrices that actually represent just some color codes IN points that have a methematical meaning in order to clasify them in 2 categories?

Probably someone can explain me this in a 2D example because any graphical representation i see it's just 2D, not nD.