Please explain in the simplest, most jargon-free English possible, the "universal property of fold"?

I am working through "Real World Haskell", which led to to a free PDF called "A tutorial on the universality and expressiveness of fold". It makes the point that a "fold" is "universal". I am wrestling with his definition of "universal", and would like to hear the from those who have already invested time digesting it: Please explain in the simplest, most jargon-free English possible, the "universal property of fold"? What is this "universal property", and why is it important?

Thanks.