A supergiant star forms when a main sequence star runs out of hydrogen atoms in its core. The star may begin to fuse helium atoms, and the change in heat and pressure can cause the star to expand many times its original size, creating a supergiant.
An ordinary star is powered by the fusion of hydrogen atoms in its core. When this supply of fuel is depleted, the star loses the outward pressure necessary to maintain its size. The star collapses slightly, and this triggers hydrogen fusion outside the core itself, causing the star to expand. If temperatures reach a high enough point, a helium flash occurs, and the star begins to fuse helium instead of hydrogen. This produces an enormous amount of heat and pressure, expanding the star well beyond its original radius.
Supergiants come in red and blue varieties. Red supergiants usually begin as massive stars whose fusion furnaces burn through the remaining hydrogen and helium at an accelerated rate. A red supergiant usually explodes into a supernova at the end of its life cycle. Blue supergiants burn at a slower, more controlled rate. A star may even cycle between red and blue over its lifetime, becoming a so-called yellow supernova like Polaris in between cycles.