I don't know. So I wrote to my old pal Matt, Scientist, and he replied:
Re the potato-- the directions are going to tell you to stick two metal
pins into the potato, and they are two different kinds of metal.
The power comes from these metals turning into metal ions and
electrons. The electrons go to power your device.
(The metal ions stay in the spud so you shouldn't eat it
because it will have unhealthy amounts of zinc or copper.)
What the potato does is provide a conductive solution, and you could achieve the same result using the same metal electrodes in a pickle or a glass of club soda, saith Dr. Science.