They're urine analysis sticks, available at least in the U.S. in any drug store (also available widely online). They tell you whether or not you are in "ketosis," the state promoted by Atkins and other LC gurus as the indication that your body is burning fat for energy, which of course is preferred.

There's a lot all over these boards about ketone sticks - some use them, some do not. I went several months into LC without ever using them, but I've since found they are a useful tool for indicating when, for me, even a SMALL amount of carbs can have a negative effect on my fat burning. It helps keep me honest.