Simply put, density is mass per unit volume.
Re: Plates and stuff-
I would show you my skills of an artist, but in a post here I cannot. Besides I am too lazy. The rock that floats above the mantle is less dense. Else it would sink. Now heat from the earths core is brought to and travels through the mantle via convection. Convection is really the circulation of heated material. The convection currents move to the topmost layer of the mantle, and as they do, the crust moves too. Simple. You see this if you put something that floats in water, and then heat it. As it moves, so does the floating object.