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.
cooking.stackexchange.com/users/11095/Ellie
I use it for hard cheeses such as Parmesan and Romano.
It grates it quite fine for things like pasta.
cooking.stackexchange.com/users/9210/Adele C
This side is ideal for zesting and fine grating of hard items (ginger is my regular task for this) and can be used much more cleanly and easily with the addition of cling wrap.
To use, you pull cling wrap around that side, then grate; you will be able to collect the result much more cleanly and completely by just peeling away the cling wrap.
A micro-plane grater is good, but this method will work in a pinch.
cooking.stackexchange.com/users/15/mfg
AS others have said its for grating hard things very finely, but not just cheese!
personally I use mine most for grating nutmeg.
cooking.stackexchange.com/users/11013/jk.
I use the star side of the grater to grate sweet potatoes to make a sweet potato pudding.
However, it must be the star side with the larger holes, 7 across the top and bottom and 15 along both sides.
I'm 64 yeas old, and its an old recipe from my father.
cooking.stackexchange.com/users/42056/Linda Lassiter Lucas
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!
What's this "pucker" style hole on my cheese grater for?
cooking.stackexchange.com
<equipment><cheese><grating>
cooking.stackexchange.com/questions/25492
cooking.stackexchange.com/users/725/TJ Ellis
This side can be used to grate hard cheeses, nutmeg, lemon zest, ginger and other hard items. It can also be used to grate sweet potatoes for a pudding. It is used for grating very hard things like lemon zest or nutmeg.
It is used for grating very hard things like cheese, nutmeg or lemon zest. You can grate sweet potatoes.