Who is this explainer aimed at? If you can understand the first sentence, you probably already know what an eigenvalue is.
The thing about Higham is that he's sort of a one-man Wikipedia of linear algebra. Many of the terms that he uses also have their own pages that (eventually) break the concepts down into comprehensible terms.
See https://nhigham.com/index-of-what-is-articles/ for a useful listing. Or, in an alternative form, https://github.com/higham/what-is . Notice that if you go all the way back up the rabbit hole you'll find user-friendly articles like "What is a matrix?" that clearly define the terms used farther down.
I really dig Higham's pedagogic style, in case it's not obvious.