The weight per cubic foot (in imperial measurement) of a foam. With some types of foam such as polyfoam and memory foam, density is an important part of quality. Good Quality Memory Foam is usually over 5 lbs/ft3 and high-quality Polyfoam (HR grade) is 2.5 lbs/ft3 or higher.
Note that comparing different types of foam of different densities in terms of quality is meaningless.