NERF stands for “Non-Expanding Recreational Foam” and the brand was originally created by the company Parker Brothers. Hasboro currently controls the NERF brand.
Taken from the Wikipedia page: http://en.wikipedia.org/wiki/Nerf
"Nerf foam is made from a solid, spongy cellular material. Polyester resin reacts with a compound while CO2 is simultaneously released by another reaction. It is this gas that creates open pockets within the polyurethane that, in turn, makes the material soft and light."