Fuel is the burny stuff you see in a lot of OE-Cake videos. It burns. It's a solid material that catches on fire when exposed to Hot. Fuel can be added to any material to make it burn. As Fuel burns, it disintegrates as particles disappear. Fuel is responsible for the Fire animation in Shader and Blob mode.
Fuel is often used to make Levels harder, by mixing it with the User element. You can pour or inflow liquid Fuel, or create it by pressing esc + F + esc. The Fire material is simply liquid Fuel + Hot. Although you cannot Inflow the Fire material, you can fake it by inflowing Fuel from something and immediately setting it on fire.
Fuel + Water is difficult to burn because it puts itself out. However Fuel and Water, with certain Parameters, create the Conductive Material for simulating electricity. Fuel + Cold makes IcyHot, a flammable material that does not evaporate water.