Giant stars are stars that have exhausted the hydrogen fuel in their cores and have begun to fuse helium. They have a lower surface temperature than main sequence stars of the same luminosity, and they occupy the upper right region of the HR diagram. Supergiant stars are even more luminous and cooler than giant stars, and they occupy the extreme upper right corner of the HR diagram.
The HR diagram is a useful tool for understanding the evolution of stars. Stars start out on the main sequence, where they fuse hydrogen into helium. As they run out of hydrogen fuel, they evolve to the giant and supergiant stages before eventually ending their lives as white dwarfs, neutron stars, or black holes.