Also called the box plots, see:
http://mathworld.wolfram.com/Box-and-WhiskerPlot.html
Many other excellent references can be found on the internet. The intent is to visually show graphically the mean (or median) of the data and the variability of data in terms of first quartile (Q1) and third quartile (Q3).
Typically, it is applicable when there is sufficient and related data for a particular interval of time and the variability (range) of this data is of interest. The focus in generally is a time trend in the data.
Changes in stock market prices or other economic/ financial analyses can use box plots. An example can be the selling price of automobiles per month because perhaps the median price is going down, but the high priced cars (Q3) is going up.