A fuel cell is an eletromechanical device that seperates fuel (such as oxygen and hydrogen) and in the process produces electricity. In mid-1800's, Sir William Grove discovered that using reverse eletrolysis on water could generate eletricity. In 1889, two researchers, Charles Langer and Ludwig Mond, officially coined the term "fuel cell" using air and coal gas. In 1932, Francis Bacon successfully developed a fuel cell device with a hydrogen-oxygen cell using alkaline electrolytes and nickel eletrodes. However, it would be more than 25 years later in 1959, he would be able to demonstrate a practical five-kilowatt fuel cell system. In the late 1950's, NASA began to fund various fuel cell research programs in hope of a power source for space missions. Fuel cell have since been used in several missions successfully. In recent years, auto manufactuers have began researching fuel cell vehicle (FCV) technologies. Some have working prototypes while others have already began shipping FCV's in limited quantities.
A Hyster Fuel Cell Power Module For Forklifts 
There are many types of fuel cells, classified by the type of electrolyte they use. These include Alkaline (AFC), Direct Methanol (DMFC), Molten Carbonate (MCFC), Phosphoric Acid (PAFC), Proton Exchange Memberane (PEMFC), Regenerative (RFC), and Solid Oxide (SOFC). One of the most promising of these is the Proton Exchange Membrane Fuel Cell. A typical PEMFC might look like this:
Parts of a PEM Fuel Cell 
Pressurized hydrogen gas enter the fuel cell on the anode side. It is forced through the catalyst by the pressure. As it comes into contact with the platinum in the catalyst, it is split into H+ ions and two electrons (e-). Only the positively charged ion can pass through the Proton Exchange Membrane, thus forcing the electrons to "go around" through the anode to the cathode, powering an external device (such as a motor) along the way.
On the cathode side, oxygen gas is also being pressurized into the catalyst, where it forms two oxygen atoms (O2). Since their charge is negative, it attracts the positive hydrogen ions from the other side of the membrane. The hydrogen ion combine with the oxygen atom to form a water molecule (H2O).
This reaction produces about 0.7V in a single fuel cell. Thus many seperate fuel cells are combined to form a fuel-cell stack. Recent advances have allowed enough fuel cells to be installed in vehicles to function as their main power source.