you can view appstate as a function that gets execute prior to your testcase. appstates are usually used when you want your AUT to be in a specific state prior to running testcase.
A perfect example would be:
You are testing that a registered user can post a message on the message board.
All your testcase does is types something in the text box an hits 'Submit' button.
In this case, an appstate could be used to authenticate a user to the message board to grand him/her rights to post a new message.
Hackers, I have to agree with Brian, you gotta read the help topics and do a search on this site before posting a question. Chances are this question has been answered a good number of times.