Simple, the Sun isn't on fire, it's a nuclear reaction.

The Sun is made up mostly of Hydrogen. Under the intense pressure the sun generates by it's own gravity, it's core is crushed into an incredibly dense and hot state.

In the core Hydrogen atoms are so close together, and move so quickly that they are able to overcome their repulsive forces (like trying to push two positive ends of a magnet together) and smash together forming a heavier element, Helium. This releases a tremendous amount of energy in the form of heat and photons (light) and is what powers the Sun.

This process is so energetic, and requires so little fuel (compared to a fire) that the Sun will keep fusing Hydrogen for Billions of years.

In larger stars this process keeps going and Helium can fuse to produce heavier elements like Oxygen, Nitrogen, Carbon, and Iron. This is where all of those elements are created. When those stars die in explosions called supernova, their enriched guts spew across the galaxy to form new planets and solar systems.

So it turns out, you are made of Star Dust