Both are hypergolic , meaning the stuff explodes on contact with each other instead of needing a pilot light or other ignition system as do other chemical fuels. This means one less point of failure and one less maintenance nightmare on your spacecraft. Being hypergolic also prevents large amounts of fuel and oxidizer accumulating in the nozzle, which can cause a hard start or engine catastrophic failure (fancy term for "engine goes ka-blam!"). It is also non-cryogenic, liquid at room temperature and pressure. This means it is a storable liquid propellant, suitable for space missions that last years.
The "special material" is thought to be a substance called " FOGBANK ", an unclassified codename, though it is often referred to as " THE fogbank" (or " A Fogbank") as if it were a subassembly instead of a material. Its composition is classified, though aerogel has been suggested as a possibility. Manufacture stopped for many years; however, the Life Extension Program required it to start up again – Y-12 currently being the sole producer (the "unique facility" referenced). The manufacturing process used acetonitrile as a solvent , which led to at least three evacuations in 2006. Acetonitrile is widely used in the petroleum and pharmaceutical industries. Like most solvents, it is flammable and can be toxic. 
The anode, the negative post of the fuel cell, has several jobs. It conducts the electrons that are freed from the hydrogen molecules so that they can be used in an external circuit. It has channels etched into it that disperse the hydrogen gas equally over the surface of the catalyst. The cathode, the positive post of the fuel cell, has channels etched into it that distribute the oxygen to the surface of the catalyst. It also conducts the electrons back from the external circuit to the catalyst, where they can recombine with the hydrogen ions and oxygen to form water. The electrolyte is the proton exchange membrane. This specially treated material, which looks something like ordinary kitchen plastic wrap, only conducts positively charged ions. The membrane blocks electrons. The catalyst is a special material that facilitates the reaction of oxygen and hydrogen. It is usually made of platinum powder very thinly coated onto carbon paper or cloth. The catalyst is rough and porous so that the maximum surface area of the platinum can be exposed to the hydrogen or oxygen.