This is a Fingered Citron, or "Buddha's Hand", a fruit from China, only quite rarely available in the U.S:
It's a citrus fruit, with little or no pulp, just rind. Although you can eat the rind candied, it's most often used as a kind of "air freshener," or in folk medicine. I paid 50 cents for it at the local Giant because nobody knew what it was. I bought it just because I thought it would be cool to have around. They had a half dozen of them and nobody in the store knew where they came from or what they were. Now it's sitting in my kitchen, freshening the air.
It smells nice and the smell gets pretty strong after a day or two, so it does perfume the air. I kept mine around for about a week, at which point it started to get brown.
The supermarket has figured out what they are, and they now charge $8.99 a pound for them!