It's not a soap dish (unless you use Motel 6 soap exclusively; too small).
This is a Japanese ginger grater. One of those wacky, single-purpose gadgets we acquire because of their cuteness, because of their brilliance, because we're hopeless gadget collectors, and there's a huge stash of brilliant but seldom-used gadgets in the lower cabinet, down there in the bin behind the rice cooker.
I may even be a more hopeless gadget collector than most, because I've got two ginger graters. The other one is made from ugly, yellow-tinted aluminum, and I find it too metallic-feeling in my hands (nothing technical, just an esthetics judgment), but boy does it have sharp teeth — it gets the job done.
I got this approachable-looking, white ceramic grater second. Actually, because it has less sharp teeth, I can scrub a knob of ginger against those teeth almost to the last molecule of ginger, without hurting my fingers.
Are you following? If you've never used one, here's the drill: Peel a chunk of ginger, and then furiously rub it back and forth (or up and down) over those bumps. Most of the stringiness of the ginger remains in a clump in your fingers, and the tender meat of the root purees into that pretty little device. A quick swipe with the fingertip clears most of the pulp off the teeth and into your dish.
So. I fetched this little beauty out of the bin behind the rice cooker yesterday, because we were warming up a batch of lump crabmeat that would be flavored with ginger and garlic. Once having rubbed the ginger into submission, I thought (oh, darn, you're way ahead of me here!) "Why not see how this baby works on a clove of garlic?"
Perfect. Just peel the paper off the clove. You don't even have to trim off the crusty little root end, because you will hold that end in your fingers and begin by rubbing the pointy, sun-facing tip of the garlic. You'll be able to puree nearly the entire clove before your fingers start bumping into those smooth, little white teeth.
And now it's no longer a wacky, single-purpose gadget. I might store it in a more accessible place from now on.