well, to me it means that I am always thinking of my topic of interest, trying to constantly see it with new eyes. It means I'll be thinking about stuff and go "I should write a paper about that". It means writing scholarly articles in your spare time because it's fun. It means being an unabashed, overenthusiastic nerd about your subject. Of course, all of those things can and should exist outside of an academic setting, but it's a lot easier for me to do those things inside of an academic setting, at a university.
Sounds to me like you should try taking the year and teaching undergrad at a college somewhere while you wait and re-apply? That should be an option at your education level. The pay won't be great, but it'll be in-field and in academia. Is it too late for you to start looking for adjunct/part time positions? Sorry to hear, spoons. Rejection sucks.