A Hertzsprung-Russel Diagram is more commonly referred to as an H-R Diagram. It is used in astronomy to diagram out the life cycle of stars. It is a standard graph with an x and y axis.
On the x-axis is the star temperatures. The goofy part of the temperature axis is that the farther to the right a user looks along the axis, the colder the star temperature is.
The y-axis is star luminosity (brightness). The higher up the y-axis, the brighter the star.
So the chart would display a very bright, very hot star in the upper left. A very bright, cool star in the upper right. A very dim, hot star in the lower left. A very dim, cool star in the lower right.
An HR diagram also shows a "main sequence" of stars. It looks like a big diagonal line that moves from the top left to the bottom right of the chart. Most stars fall on that main sequence line, and most stars move down from left to right as they age and use up their fuel.
I've attached a picture of a typical HR diagram in the link below.