Non-singular densities top out in neutron stars. Densities upward to 8x10^17 kg/m^3 are thought to occur. As atomic nuclei densities are ~3x10^17 kg/m^3, the neutron star is considered by some to be just a single ultra massive atom.
The density of a material is generally typical of a material. The density is it's mass divided by it's volume. So if you have something that weight 20kg and has a volume of 2500cm3 or 2.5L it's...
density is a reflection of a couple of things. 1) how heavy the atoms are (where on the periodic table) 2) how closely packed they are (what is their intermolecular interaction/ lattic structure)