Volume is like another other volume, it's a 3D region of space. In this case the region is taken to be sphere of radius r_n. And within that volume you have N number of conduction electrons.
Divide that and you get a density of conduction electrons per volume or vice-versa.
Density, in this case, refers to the number (not the mass) per unit volume. It (or the reciprocal) tells you how much room a conduction electron has 'to itself' or the space between conduction electrons.
When we talk of Population Density, we don't mean the Mass, either. It's a fairly common English / Technical use of the term density.