The nature of the distributions and some basics are described in
http://desktop.arcgis.com/en/arcmap/latest/tools/data-management-toolbox/distributions-for-assigning...
I have used them for generating point patterns, adding 'noise' to generated elevation surfaces, simulation of occurrences of phenomena in space and/or time. Distributions of various types form the foundations of statistical testing and in inferential statistics you are often comparing observations to those of a known distribution. Understanding them, might be easier if you had a particular application in mind.
