What’s a scale, and how do I use it?

People often have a difficult time understanding the point of scales; questioning why they need to learn them, how to practice them, etc. But it seems that few of the people asking these questions actually get satisfying (or comprehensible) answers. Isn’t there some simple way to explain it? Isn’t there some way that a total beginner can see how learning scales will impact their playing and understanding of music?

Yes, there is… now that I did it.