I love this word. It is what you call the coffee cup sleeves that you get at places like starbucks.
Coffee is sometimes served in a cheap and disposable white plastic cone, without a handle and too thin to allow one to hold it with hot coffee. It snaps into a holder that has a handle. What do you call that holder?
(Bonus: What is the mark left on the table by a moist glass?)
Our language seems to be in the process of co-opting the word zarf for this.
A zarf is "a metallic cuplike stand used for holding a finjan", and a finjan is in turn "a small coffee cup without a handle, such as is held in a cup or stand called a zarf". These terms come from the middle east.
On several sites on can find "zarf" more generally as any holder for a handleless coffee cup. In dictionaries sites, though, the closest I find to that broader use is Grandiloquent Dictionary (on-line): "zarf – a special sleeve for a coffee cup or a beer can". Mrs. Byrne's Dictionary (published; not on line) lists "zarf – a cuplike holder for handling hot coffee cups (Arabia)"
Bonus: culacino – the mark left on the table by a moist glass