As Eilenberg-Mac Lane first observed, "category" has been defined in order to be able to define "functor" and "functor" has been defined in order to be able to define "natural transformation".
Saunders Mac Lane, Categories for the Working Mathematician
Is there a way to explain that to a non-mathematician?
People want to tell everything instead of telling the best 15 words. They want to learn everything instead of the best 15 words. In this thread, instead post the best 15-words from a book you've read recently (or anything else). It has to stand on its own. It's not a summary, the whole value needs to be contained in those words.
I'll start in the comments below.
(Voted by the Schelling study group as the best exercise of the meeting.)