Cutouts are for when you tell the renderer to use one object to literally cut out another. It's for when you render multiple CG elements on different layers to be assembled in compositing.

Let's say you're rendering a scene with 3 characters in a kitchen. You're going to want to render each of the characters on their own render layers, as well as the environment on its own layer too, to make things easier.

So when you go to composite everything together, you put the characters over the background. Easy, right? Well, what happens if one of the character walks around behind the kitchen table so his legs are obscured behind it? Now you can't just slap the character over the background because he's supposed to be behind the table.

What you'd do here is put the table into the character's render layer as a cutout. Now when the character passes behind the table, the table cuts him out (literally, his legs aren't rendered into color or alpha) so he will layer properly in Nuke.

Now, let's say the other two character in the scene hug each other, with their arms wrapping around each other. These two characters are on their own render layers, but you can't just put one over the other in the composite, because they're wrapping around each other (this is called an over-under situation: where one layer is literally behind and in front of another layer at the same time). You have to render both characters with each other as a cutout, so when you layer them together in the composite they layer properly.

And in case you're wondering "why don't I just render everything in one layer?" That's not a very good practice. Breaking things apart into different render layers makes things much easier to work with, and can save you render time.