There are two kinds of density, "weight density" and "mass density". We will only use mass density and when we say: "density", we will mean "mass density".
Density is mass per volume. Lead is dense, Styrofoam is not. The metric system was designed so that water will have a density of one gram per cubic centimeter or 1000 kilograms per cubic meter.
Lead is about 10 times as dense as water and Styrofoam is about one tenth as dense as water.
here is a link for further explaination of density
here is a link of a animation on how density of an object causes it to float or sink in water.