A fuel cell uses a chemical process to generate electricity. At the anode of the cell hydrogen is broken down into protons and electrons. The protons diffuse through a membrane to the cathode.
However, the membrane is an electrical insulator so the electrons are forced to travel round to the cathode via an external circuit. This is the electric current generated by the fuel cell.
At the cathode, the protons and electrons react with oxygen to form water, the only emission.