Solar energy comes mostly from fusing 4 hydrogen nuclei (protons) into a single He-4 nucleus. About 90% of that energy is being generated in the deepermost 10% of the Solar core, since that region has high enough temperature for the reactions to be significantly effective.
Convection, on the other hand, is absent in the most of the Solar interior, so there is no circulation of fresh hydrogen, providing new fuel for the core to burn it. So the core is getting enriched by the He-4 nuclei, which the Sun mostly cannot fuse further because the temperature is not that high.
At some point in about 4-5 billion years, once the core becomes too hydrogen-poor, the effective burning will stop. Internal pressure will no longer be high enough to prevent gravitational collapse, and the Solar core will start to contract under its own weight until a temperature of 100 million Kelvin is reached. At that point the helium burning will ignite, fusing He-4 nuclei into oxygen and carbon.
The shell just above the core, on the other hand, will start to effectively heat up and burn hydrogen. Due to the excess of pressure from hydrogen fusing, the shell will inflate and the Sun will become a red giant.
The core will consume helium, until only carbon and oxygen nuclei are left deep inside. At that point the core will contract further forming a white dwarf, slowly burning the rest of the fuel for another trillion years, until it cools down to become a black dwarf. Of course, today there are no black dwarfs known, since the Universe is not old enough yet (~14 billion years).
The spherical envelope will most likely expand further, decoupling from the core and forming a planetary nebula.