The idea in all the examples in this page seems to be: write a string with some code and then write some more code that processes the string in a way that when the string is finally output it contains the variable assignment (of the string), the variable contents, and the later program code.

Indeed that is what the first wikipedia example does

a = 'a = {}{}{}; print(a.format(chr(39), a, chr(39)))'; print(a.format(chr(39), a, chr(39)))

I dunno, my explanation seems to make more sense in my head than the analogy this article fixates on of a machine that can build a machine etc