I was just grating some mozzarella cheese for dinner and a question came to me. I always use one side of my box grater. I don’t use the other 3 sides. In fact, I don’t even know what they’re even intended for. It’s not the kind of thing that comes with an instruction manual, so any experienced kitchen folk have a clue what their point is?
the other wide side has smaller holes for finer grating. One narrow side just has raised sharp piercing, it is for shredding, it looks like a Ginger grater. I forget what the 4th side is for, I think it’s the same as the other ginger grater side.
For grating things in different sizes. 
You’ll notice that each side has different sized holes. You want thick, medium or really skinny cheese? The one that is really fine and feels like sandpaper is for hard stuff like parmesan cheese, nutmeg, cinnamon, etc.
Side #1 (the most commonly used side): For grating soft cheeses like cheddar & mozzarella, potatoes for hash browns.
Side #2 (the finer version of side #1): for grating hard cheeses like parmesan & romano.
Side #3 (slit opening): Obviously for slicing, but cheese doesn’t seem to work very well here. I guess maybe you could get potato slices out of it for baking into potato casseroles.
Side #4 (Lots of sharp dimples): For scoring fruit rinds & making lemon/lime zest.
YMMV.
I use the “slit” opening on the side for shredding lettuce. Works well.