A fuel is any material that can react to release energy from a potential form into a usable form. In most cases this is just something that will burn.

For example, coal was burnt by steam trains to heat water to provide power, and natural gas is burnt to provide heat to run power plants. However a fuel is not necessarily combustible. For example, in a nuclear reaction a fuel will undergo fission. This still provides a useful source of energy but not via combustion.
Also, in stars (and our sun), hydrogen is the fuel for the nuclear fusion.

In the bodies of most animals, the fuel sources are carbohydrate, fat, protein, which supplies the energy for muscles.