Geonyte is a type of energy supposedly provided by "Spirit Trees," or Mocks. In Monster Rancher 4, geonyte is used as fuel to power your Training Gadgets and help your monsters gain higher stats. Geonyte is mentioned again in Monster Rancher EVO as a type of fossil fuel used to power lights and carriages. There is a similar lifeforce element called Anima (the difference being that geonyte is more like a natural force and anima is more like a soul).
It is likely that the fuel cell of the Iron Bird (called a spirit capsule) seen in the anime series is powered by geonyte (perhaps all training gadgets have a spirit capsule?).