What does the indicator on Settings>Privacy>Facebook mean on an iPhone
Settings->Privacy lists the social accounts that iOS can store info for. If you go into one of them, such as Facebook, you will see a list of individual apps on your phone that want to access those accounts to do the following:


Create a network session. 
Get the activity feed for a user. 
Make a new post. 
Set properties on a post, add attachments, etc. 
Publish a post to an activity feed.


If the toggle next to the app is green, then you have given permission to that app to do these activities. If the toggle is not green, then the app has requested permission, but you have denied it.

It is interesting in that Facebook is also listed as an app looking for Facebook data.  This lets it keep using the login and password you've entered if you've shared something on Facebook from another app.