It appears from TOS that the intent of the "non-interference" directive was to prevent Starfleet from sticking it's nose in where it didn't belong. Don't try to overthrow an alien government simply because their way of life was contrary with Federation values. Don't interfere with their elections or leadership.
Like today. The ideal is that the United States doesn't interfere with the internal workings of Russia or Jordan or Lybia or whatever. Yes, they do attempt to do so clandestinely, but the image presented is that everyone is allowed to live their own life the way they see fit. Yes, the Federation (or the United States) is there to help in case of disasters or such. Overall, though, your world is your world (or nation or government).