When stars run out of hydrogen, their cores shrink and heat up, and eventually start to fuse helium nuclei together. The helium reactions release energy at a much higher rate than the hydrogen reactions, which makes a star appear more luminous. The larger flow of energy also pushes the outer layers of the star further outwards, making the star bigger, but cooler and redder. The result is that stars fusing helium in their cores appear in the upper right-hand portion of the HR diagram. We call these large, luminous but cool stars RED GIANTS.
A modern HR digram showing the positions of the main sequence, giants and Dwarfs Way.
The ability to read the evolutionary state of a star off its position on the HR diagram had profound implications for astronomers. For example, you can use this evolution on the HR diagram to estimate the age of a cluster of stars. Clusters form stars all at once, massive and low-mass stars simultaneously. If you look at a young cluster, all the stars will appear on the main sequence, because they are all still fusing hydrogen in their cores. As the cluster ages, the massive stars will run out of hydrogen and move off the main sequence towards the giant branch. As time passes, more and more stars will leave the main sequence. After a very long time, only the least massive stars, down in the lower-right corner, will still appear on the main sequence.
An HST of the globular cluster M15, which is 40,000 light-years from Earth in the constellation Pegasus. The stars in M15 are approximately 12 billion years old and are some of the first stars to form in the Milky Way.