So we're looking for an introduction to transfinite ordinals. I'll be assuming that you don't want hardcore maths books!
The closest things to a classic is probably "Infinity and the Mind" by Rudy Rucker, Rudy Rucker (npub1dsw…7akd) . Chapter 2 is especially relevant.
Eugenia Cheng's recent "Beyond Infinity" is extremely accessible and fun, but it doesn't go as far beyond infinity as my whiteboard (or Rucker).
This blog (and the two posts that follow it) is also good:
https://johncarlosbaez.wordpress.com/2016/06/29/large-countable-ordinals-part-1/