How does the Marching Cubes Algorithm Work?

So, I'm trying to make a low poly procedural generated terrain using Unity 5. (Something like this video)

I read this article (well, at least tried to read): http://paulbourke.net/geometry/polygonise/ I didn't understand most of it.

I'm quite a beginner at this, and I'm starting to get really confused. I currently know how the marching cubes algorithm is commonly used. (I understood the first part of the article)

However, i'm unsure of how the algorithm marches a cube around every point in 3d space that it is told to display, and then scans vertexes of each piece of land to somehow work?

So, I'm wondering if anyone could direct me to some more simple explanations of the algorithm.

I'm not very good at creating a mental picture of things, So I would really love some examples of the algorithm being used in Unity as well.

Thanks