This is a mile-high, extremely oversimplified view of machine learning, but this idea helped a lot of various machine learning approaches click for me.
You start with very complicated data. You need to distill it down so you can plot it in space. There are all sorts of techniques to do this distillation. Once you can plot your data, you can do all sorts of math magic. There are lots of different types of math magic. The math magic lets you calculate distances between points and find clusters. Voila!