The map displays two things.

Firstly - the average temperature for that state during the month of July 1936, based on data collected from weather stations in that state. Secondly the colour shows how different the July 1936 temperature is from the long term average of temperatures in July. If it says "record warmest "then that record should still hold today (or at least when the map was made). The map and some more information on the 1936 heatwave can be found here http://www.weather.gov/ilx/july1936heat

If you have more questions you might want to try /r/askscience