Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.
The class determines the cost of the shipping. The lower the class, the lower the cost.
Density is the relationship between weight and size. A ping pong ball, which is very little material surrounding a good amount of air, is low density. Bricks, which are heavy for their size, are high density. In LTL shipping, it is commonly measured in pounds per cubic foot.