A meteorite is simply an object that has entered another bodies atmosphere (in this case planet Earth) and survived travelling through the atmosphere to impact the ground. An asteroid never impacts another bodies atmosphere, and has no atmosphere itself. An asteroid can range in size from small to very large, and even have their own moon/s.
Edit - to simplify the difference, they are both basically the same thing, both originating from space, they are separated only by location, an asteroid stays in space, a meteorite is what hits the ground.
Edited by Sky Scanner, 17 February 2013 - 09:31 PM.