It's a knife with a slightly curved tip. You use this to seperate the flesh of each segment from the skin of the segment. The grapefruit is cut in half, you can put sugar on it if you want to (I let it stand for at least ten minutes, with a good layer of sugar which is then absorbed), then put the knife between the endocarp and the meat and cut until the bottom, following the skin. Also seperate the flesh on one side of the segment, but let the other side sit. Repeat until you have done so for all segments. Then use a normal, small spoon to eat the inside of each wedge, without the icky skin.

And now I'm hungry...