It sounds like it may be nail fungus. It is very hard to treat with topical products though some progress can be made with persistence and time. Fungi-nail is a liquid application that may work. There are oral tablets that work better but rather expensive and require a doctor's order. Is it on your big toe? Most often it is the big toe.
Fungi... Just clean your feet (toenails) more often. If after you shower, there's still more 'white stuff' under your toenail, try to clean it then, for it will be easier since it just got soaked in water.
Could be fungus, dead skin or sock fuzz. Usually fungus makes your toenail look nasty too. Wash your feet and dry them really good when you shower. If it's fungus, you can soak your toe in Listerine. It sounds weird but it kills the bacteria. If it gets really bad I would go see a foot doctor.