A picture is worth a thousand words: https://en.wikipedia.org/wiki/De_Bruijn_index#/media/File:De...

It's literally just notation:

- It doesn't matter how you name variables. (if you want to sound cool: "lambda terms are invariant under alpha-conversion")

- Each new variable introduces a scope.

- Therefore, how scopes are nested defines the entire expression.

- Instead of the usual way, we represent scopes with numbers, with the index representing "how nested the scope is". Imagine it's python, and you're pressing tab that many times.