In approximately 5 billion years, the sun will begin the helium-burning process, turning into a red giant star.

What is an example of a red supergiant star?

An example of a red supergiant star is Antares. 119 Tauri, Betelgeuse, Mu Cephei, Stephenson 2-18 and VV Cephei are other famous examples of red supergiants. Most red supergiant stars explode as supernovae, but some of the brightest become Wolf-Rayet stars before exploding. They are stars that have a LOT of light.

Why won't the Sun become a supergiant?

The Sun's mass isn't large enough to become a supergiant star, so it can't undergo a Type II supernova explosion. Our Sun will only become a White Dwarf star in the future. Since our Sun is not in a binary system, once it becomes a white dwarf, it won't accrete matter and will not undergo a Type Ia supernova explosion.