[petuniasevan]

It's not burning, as such. "Burning", or oxidation as it is more accurately called, is a chemical process which can be either

• The loss or removal of electrons from an atom, ion or molecule

  or

• The gain or addition of oxygen by an atom, molecule or ion.

  On the other hand, the Sun and all stars are huge balls of mostly hydrogen gas (with a little helium and a dusting of other elements). Oxidation does not come into play here. The core of a star is under extreme pressure and temperatures are in the tens of millions of degrees. This allows the process of nuclear fusion to take place there.

  Nuclear fusion is an atomic reaction in which many nuclei (the centers of atoms) combine together to make a larger one (which is a different element). The result of this process is the release of a lot of energy (the resultant nucleus is smaller in mass than the sum of the ones that made it; the difference in mass is converted into energy by the equation E=mc₂). Stars are powered by nuclear fusion, mostly converting hydrogen into helium. In the most common process, the proton-proton reaction, 4 hydrogen nuclei combine to form a single helium nucleus; about 0.3% of the original mass is converted into energy.

[BradyLS]

Thanks for the answer, Petuniasevan! I understand the process much better now.