Polyurethane is a type of polymer, which means it is essentially a large chain of smaller molecules. Chemically speaking, polyurethane is a group of organic units (organic units all contain carbon) that are linked together by a urethane . In technical terms, a urethane group is a nitrogen that is attacked to a carboxyl group. One of the advantages of polyurethane is that its properties can be easily altered by making simple chemical adjustments so that its strength, stiffness and density are highly variable.
Polyurethane is called a reaction polymer, which means it can be made as the result of a chemical reaction. In order to make a urethane bond, you have to have an isocyanate group (which can be drawn out as -N=C=O) and an alcohol (-OH). These two groups will, under certain conditions, react to form a urethane bond. In order to make a polymer using urethane bonds, each sub-unit must have an isocyanate group at one end and an alcohol at the other. This way, not only will individual sub-units be able t link up and form urethane bonds, but small clusters of two, three, or more sub-units can also bond to allow many urethane bonds to be made quickly.
The most common usage of polyurethane is in making foams. If the polymer is made at a high temperature, it can be made to stay liquid. Then, small amounts of air can be blown in to make bubbles, allowing for a soft, padded foam. By changing the chemical composition of the organic subunits, the of polyurethane can be altered--allowing it to be softer or harder, more or less flexible, and even change the temperature at which it becomes pliable. This is the concept behind memory foam, which becomes softer and more moldable at temperatures slightly warmer than room temperature. This allows it to form a mold around warmer objects.