Density is a measure of mass per volume. In SI density is measured as kg m-3 (kilograms per cubic metre), but many people use the more convenient g cm-3 (grams per cubic centimetre) or (equivalently) kg l-1 (kilograms per litre). The higher density, the higher mass per volume.
Formerly mass and volume were linked by defining the gram to be the mass of one cubic centimetre of water at 4°C which meant that water had density 1 kg/litre. However, using one cubic centimeter of water as a standard for one gram is problematic due to the possibility of mass loss from evaporation as well as changes in density with temperature. For this reason alternate definitions of the metre and kilogram have been developed, which can be reproduced more reliably in a laboratory. Because of slight changes in the metre and kilogram due to these new definitions, the density of water at 4°C is not quite exactly 1, but 0.99995 kg/litre. A cubic metre of water thus weighs approximately one metric ton.
1000 kg m-3 is 1 g cm-3.
The perhaps highest density known is reached in neutron star matter. A black hole, according to current theories, does not have any volume, and its density can be seen as either infinite or non-existent.
This use of density is also known (if you follow ISO 31) as volumic mass (that is, mass divided by volume).
Density may denote how much of a certain substance, object or occurrance is present within a certain area or volume. Often used is population density, meaning how many people on average live in an area (usually persons per square kilometre).