A fuel cell combines a fuel (hydrogen or hydrogen source) with an oxidizer (oxygen or air) to produce electrical power. When atoms of the two gasses hydrogen and oxygen are put next to one another, they spontaneously combine to form water. This combination results in the release of a lot of energy and lets an electron loose temporarily. They never run down or need to be recharged.

A fuel cell converts hydrogen and oxygen into water, producing electricity and heat in the process. It has two electrodes, the negative anode and positive cathode, separated by an electrolyte that only allows specific ion flows. Fuel is delivered to the anode and oxygen to the cathode. In a fuel cell, the electrode is not consumed, and the cell can produce electricity as long as more fuel and oxidizer are pumped through it.

In a fuel cell, the hydrogen and oxygen are separated by a membrane. The membrane captures the free electrons during the chemical reaction that forms water, which in turn powers anything hooked up to the fuel cell. It also releases some heat.

Fuel cells are a remarkable power source. They store energy in two naturally occurring elements (oxygen and hydrogen) and form a single waste product (pure water). Refueling a fuel cell means providing more hydrogen and oxygen. With an external source of electricity such as a solar panel, one can split the waste water back into its component parts and use it again as fuel.

Fuel cells can use hydrogen directly, or they can obtain hydrogen from another fuel, like liquid methanol (wood alcohol), which is renewable and can be transported more easily than hydrogen. 

Unfortunately, fuel cells are very heavy and it takes a fair amount of propulsion fuel to place one into space. Fuel cells that are large enough to provide energy for very long space missions would require a lot of fuel or an external power source to provide energy to resplit the water back into hydrogen and oxygen. Lots of fuel is expensive to get into space, and an external power source means adding solar panels.

Source : https://www.nasa.gov/centers/glenn/technology/fuel_cells.html

 PEMFCs 

RFC  

SOFCs 

Source : https://www.nasa.gov/centers/glenn/technology/fuel_cells.html

So overall the reliability , long duration output , safety , efficiency, weight and lifetime of fuel cells meet the requirements of Apollo  the best .

NASA selected alkali fuel cells for the Space Shuttle fleet, as well as the Apollo program, mainly because of power generating efficiencies that approach 70 percent. Alkali cells also provide drinking water for the astronauts. The cells are expensive -- perhaps too expensive for commercial applications -- but several companies are examining ways to reduce costs and improve the cells' versatility. Most of these alkali fuel cells are being designed for transport applications.


Source:
http://americanhistory.si.edu/fuelcells/alk/alk3.htm