Your hands are dirty. In fact, the CDC has some very interesting statistics about just what ends up on your hands and why that matters (read: lots and lots of poop). This is why hand cleanliness is so important and when you're in space the same rules apply. Don't risk spreading germs to alien species and taking down intergalactic empires.
Since there's no running water on the ISS (for obvious reasons), a Squeezable "No Rinse Body Bath" pouch is used instead.
In this video, former International Space Station Commander Chris Hadfield shows us how things are done when it's time to wash up for dinner.