An H-R Diagram (HRD) is a plot of Effective Temperature versus Luminosity (or Absolute Magnitude, effectively the log of luminosity) on a log-log scale. The modern H-R diagram is an outgrowth of tables and charts in the work of Ejnar Hertzsprung and Henry Norris Russell.
H-R diagrams are used to summarize the characteristics of stars by plotting each of a number of stars, but a plot point might also be used for whole groups, such as galaxies to characterize the differences in the stars of different galaxies.
H-R diagrams are a starting point in applying stellar theory to individual stars. The diagram clearly shows the different characteristics of various phases of Stellar Evolution, such as the Main Sequence, the Red Giant branch, the Asymptotic Giant Branch, White Dwarves. Main Sequence stars generally form a diagonal line from "bright and hot" to "dimmer and cooler" whereas Giant Stars are in their own region of the diagram, both bright and cool. The separation of these regions is known as the Hertzsprung Gap, where few stars are found because they evolve relatively quickly between the main sequence to the giant phases.
Stellar Temperatures range from a few thousand Kelvin to around 40,000 (about 3 Dex, but ranging cooler if Brown Dwarves or even Gas Planets are included), and stellar luminosities from a thousandth the Sun's to a million times the sun's (about 9 dex).
H-R diagrams are often plotted of just the stars of a specific Open Cluster or Globular Cluster to display the cluster's characteristics. In this context, the term Isochrone (which means "same age") indicates a line (undoubtedly curved) that traces the positions of stars of a specific age.