For instance:
I have mysql running and I am in the midst of an insert, OS X (or the user) kills the process, does the data get inserted correctly ? What part of the insert did it stop in the middle of ? Did half of the insert work ?

Same can happen in Apache or Tomcat. Think a php script or Java class that writes an external file or goes to a database.

Shutdown procedures allow the program to clean up after itself before stopping, wait for a database connection to cease or else cease it, explicitly close or wait for files to close, etc.