To me the word means just one thing: fairness.
Life, as they say, isn't fair, but that's not an excuse for people to not be fair. In fiction, protagonists who prioritize fairness are people I want to root for. Those are the characters I find appealing and the stories I'm interested in following.
A character might not know what's fair or she might be misled about what's fair -- she might have wrong or incomplete information, for example. She might have to revise her opinion about what's fair along the way. But to be appealing to me as a reader (or author), a character wants to do the right thing. If her world is small, she might only be concerned with doing the right thing for those in her immediate environment. As her knowledge of the universe grows, her priorities shift and she gains a wider sense of what "fair" can mean.
She has to be fair to herself, too, which may be how she avoids becoming overly self-righteous or self-sacrificing. We expect our heroes to make sacrifices, of course, even sacrificing their lives if it's "worth it", but only when they're backed into a corner with no options.
"But that's not fair!" -- it's the eternal whine of children all over the world, but sometimes those children have a point. A character who considers what's fair, and is concerned with making things fair, is far more appealing to me than a character driven by selfish or petty motivations, including righteous revenge.