What's this "pucker" style hole on my cheese grater for? Ok, this picture has two sort of weird looking holes, but the one I'm asking about is on the left side of the picture - the metal sort-of puckers up, like it's been punched through from the back side.

I've tried this kind of grater to zest things before, with no success, and it clearly mauls cheeses... I can't figure out what it's for!
It is designed for the likes of hard cheeses, nutmeg, or zesting lemon and orange skin. As you mentioned,  a lot of what you want to grate or zest gets stuck between the puckers and it clogs easily.

I would really recommend getting a micro plane as it gives the same fine result without becoming clogged.