Solid graphite pencils, also known as woodless pencils, are often used for art and drawing. While a standard pencil is a thin core of graphite (well, graphite mixed with clay, generally) inside a wooden body, a solid graphite pencil does away with the wood.
Why would it be good to lack wood? If you're shading large areas, it can be useful to have a much wider stick of graphite, without the surrounding wood getting in the way. You can shade much more at once, which can help with getting a more even result as well as being faster and easier.
But won't your hands get dirty with all that graphite unprotected? Not usually, as these pencils normally have a layer of lacquer or paper to protect your hands. And sometimes you just have to risk dirty hands in the name of your art.