Our star is classified as a low mass star – more massive than red dwarf stars, but significantly less massive than giant stars.
Stars like the sun do not have enough mass to sustain fusion reactions past the fusion of helium to carbon, and thus they will never reach the faithful iron fusion stage that results in supernovae of giant stars. The sun, therefore, will never go supernova!
Instead, the sun will eventually fuse all core hydrogen to helium, and then all core helium to carbon, at which point it will not be able to fuse carbon further.
In the meantime, the outer layers of the sun will have expanded so much that the sun would have become a red giant star, and eventually it will lose these outer layers to expose its carbon core.
The exposed stellar core, which is no longer fusing at this point, is called a white dwarf.