Whenever anybody I know speaks of a "Mouli" they are referring to a kind of grater that is apparently no longer made, and is pictured in none of these links.
It stands on three retractable legs (it folds pretty flat for storing, and you store the blades separately), has several removable circular blades close to the size of food processor blades (but only the sharpness of the sides of a box grater) which slip into a horizontal slot at the bottom of a medium-shallow well.
Whatever you're grating you put into the well, and there is a fitted lid-thing at the end of an arm that goes into the well. You press down on the arm and turn a crank to revolve the blade. When the lid is all the way in and the last bit of food either goes through or slips out of the side, you're done.
I was fortunate enough to buy mine when they still sold a blade with tiny tiny holes perfect for finely grating Parmesan cheese. Later they sold the graters without that blade. There are about four blades.
This is one of the loveliest cook's tools I've ever owned. It isn't scary, it can't hurt you (know how if you aren't careful you can scrape your knuckles on a box grater?). It gives you more control than a food processor, which gets carried away and seems to be less versatile. My food processor grates carrot, for example, more thickly. And there's no vessel to clean, since everything drops onto a plate or a piece of waxed paper.
It also gives more control than a box grater (which to me has an awkward design). To apply pressure, you don't have to touch the food directly as with a box grater. It's easier to press down on an arm than to press down on a bell pepper or a carrot or a wedge of Parmesan. And with a box grater you have to clean the other three sides afterwards, whereas with the Mouli you just slip the little blade out for cleaning and run a sponge around the inside of the plastic well.
Everybody I know who has one loves it. I discovered to my horror when I wanted to give one as a gift that they can be found nowhere. I couldn't even find a second-hand one on the Internet (****, I'd never re-sell mine). Why they discontinued it I haven't the slightest idea, but discontinue it they obviously did.