I have found several algorithms that explain how to find strongly connected components in a directed graph, but none explain why you would want to do this. What are some applications of strongly connected components?
You should check out Tim Roughgarden's Introduction to Algorithms course on Coursera. For every algorithm he goes over, he explains some applications of it. Very useful, and makes one see the value of studying algorithms!
The use of strongly connected components that I remember him saying is that one could use it to find groups of people who are more closely related in a huge set of data. Think of facebook and how they recommend people that might be your friends...
This could also be used to see chunks of a population. Say, "Wow, this huge component all has the hobby of walking backwards and likes eating moldy pizza!," it could show correlation. Advertisers for moldy pizza would use this data to target people who like walking backwards. Who knows!