Why does the H-R diagram look different for star clusters of different ages?
Stars form in clusters pretty much simultaneously, however, stars age at different rates depending on their masses.
Stars form when a diffuse nebula begins to collapse due to some sort of impulse, often a nearby supernova, or some sort of gravitational disturbance. The nebulas do not collapse uniformly, but rather in dispersed clumps. Eventually each of these clumps will form stars, and the nebula will become a star cluster.
Since all of the stars in the cluster formed out of the same collapse, they will all be roughly the same age. However, more massive stars will fuse all of their hydrogen faster, and move on to later stages of stellar evolution sooner.
The image below shows theoretical H-R diagrams for star clusters of different ages. The shaded region represents the main sequence, where stars will fuse hydrogen for most of their lives. You can see that by the time the smallest stars begin fusing hydrogen, the most massive stars have exhausted the hydrogen in their cores and begun fusing heavier elements as giants and supergiants.
As time goes on, the "turn off" point moves lower and lower on the main sequence, representing less massive stars running out of hydrogen. Since this relationship exists between the mass and life span of stars, these H-R diagrams can be used to estimate the age of the star cluster.