Simple rereduce introduction tutorial

[Dmitrii Dimandt]

Does anyone have an easy-to-understand introduction to/tutorial on the 
rereduce argument in the reduce function?

I *sort of* understand why it's there and I have a vague understanding of 
how to work with it, but this understanding is just that — vague.

What I would really like to see is a couple of examples and explanations on 
how and when it should be taken into account when creating the reduce 
function