Alright, kiddo. So let's say you have a bunch of light switches in your room. Some of them turn on the lights and some don't. And you want to figure out a way to write down which switches to flip so you can turn on the lights you want.
Well, the reed-muller expansion is like a secret code that tells you which switches to flip to get the lights you want. It's a way of writing down a big complicated problem in a simpler way.
Think of it like this: you have a bunch of toys in your toy box, and you want to find a certain toy. You could go through the whole toy box and look for it, but that would take a long time. Instead, you can ask your mom to tell you which corner of the toy box it's in, and then which shelf, and then which section. And pretty soon you know exactly where the toy is without having to search through everything.
The reed-muller expansion works kinda like that. It takes a big complicated problem, like figuring out which switches to flip to turn on certain lights, and breaks it down into smaller and simpler parts. That way, you can solve the problem more easily.
Does that make sense?