Here's a simple definition from Finally Feminism 101:
Privilege is an advantage conferred by the configuration of society to some groups over other groups.What do we mean here by advantages? Let us say that an "advantage of X over Y" is a benefit X enjoys in reaching X's goals that Y does not enjoy in reaching Y's goals. So, unwinding, privilege of some group over another means that the way society is configured gives the first group benefits in reaching their goals that the second group does not receive in reaching their goals.
(Side note: It is also interesting to remove society from the definition and make another definition:
X privilege is an advantage conferred by configuration of X to some groups over other groups.So, "social privilege" would be a class of advantages conferred by the configuration of society. Meanwhile, "biological privilege" would be a class of advantages conferred by the configuration of biology to some groups over others --- for instance, men are biologically privileged with strength and not-having-babies, people without disabilities are biologically privileged over people with disabilities, and so on.
This may not be a good more general definition because it conflates with an identical use: "X privilege" means, I think, "advantage conferred to group X over group not-X by the configuration of society with respect to X." For instance, "male privilege" is advantage conferred to men over women by the configuration of society with respect to men; white privilege is advantage conferred to white people over non-white people by the configuration of society with respect to race; etc.)
"Privilege" is an empirical claim. It can be supported or disproven by observation. For instance, "men have privilege in the workforce" makes the prediction that men should have, all else equal, higher salaries. They do. So this is evidence for the proposition that society's configuration gives men an advantage in the workplace.
Privilege is a statement about groups, so it only extends stochastically to individuals. Nonetheless, since individuals make decisions based on limited information and assessments of probabilities, this stochastic extension impacts individual behavior. (Interesting implication: The perception of privilege can create privilege where none actually existed.)
Since basic human instinct is to evaluate others' situations by placing ourselves into their spots, privilege can be difficult to detect for members of the privileged group. Because of the advantage conferred by privilege, a member of the privileged group performing simple first-order analysis on the motivations and behavior of a member of the non-privileged group will fail to detect factors for which the non-privileged person must account in optimizing well-being. (More on this below.)
Privilege could be "intrinsic," in the sense that one group in society possesses a set of values or characteristics that give it an advantage over other groups. For instance, suppose that upper-middle class families have a culture that emphasizes education and long-term investment in human capital, while lower class families do not. Given a broader society that is configured to reward education and long-term investment over short-term consumption, we could say that this is an example of upper-middle class privilege over lower classes. (If this is not an example of privilege, then the definition needs to be modified to exclude this case and others like it.)
Not all privilege is good; not all privilege is bad. Some groups are privileged in some areas and underprivileged in other areas. (For example, mathematicians are privileged, apparently, in precise logical thinking, but underprivileged in social subtleties. Victorian upper-class women were privileged in their treatment by men, but severely underprivileged in freedom.) Given a group, one can probably measure all the privilege it has and all the underprivileges it has and judge whether it is net positive or negative.
In practice, what does this mean? While I was following a little bit of that Rebecca-Watson-got-creeped-on-in-an-elevator story (I refuse to call it "elevatorgate" because appending "-gate" to the end of every salacious outburst is just ridiculous -- it was the name of the hotel, people), I realized this: recognizing privilege is just modifying the golden rule.
We all know the golden rule. We learn it in preschool, taking our first steps into a larger world of social interaction. "Do to others what you want them to do to you." We tell it to our children: "Kiddo, would you like it if he hit you? Then don't hit him." It has arisen in religious and philosophical teaching independently across the world.
Why is it useful? As humans, we all have some basic beliefs in common - we want social interactions to be pleasant, we don't want to get hit, we don't want to have our stuff taken, so on. Internalizing the golden rule amounts to recognizing this commonality: we can predict other people's reactions to our behavior by placing ourselves on the opposite ends of our interaction.
But as we pass on to interaction with broader and more diverse people, our approach needs to become a little more sophisticated. Here's a motivating example. Until last spring, there was an abandoned building about a block away from our apartment. It was between us and our jobs. I hadn't really noticed it before, but my wife drew my attention to it: she wanted me to walk her home from her job. Why? Because of that abandoned building.
It would never have occurred to me to be creeped out by the building. When I put myself in her place -- which wasn't hard, because I had walked past it many times! -- I still wasn't creeped out walking past it. It was only when I modified my analysis of her motivations to take into account differences between us that I understood why she felt the building was creepy.
She's weaker than I am and can't run as fast. Her chances of being the target of an assault are much higher than mine. (They're still statistically small, given our class and neighborhood, and even smaller, but still high enough, with bad enough consequences that she needs to take them into account). So, in the exact same situation, she is rationally more cautious than I am.
To recognize privilege (if it exists), you have to modify the golden rule. When you're evaluating someone else's motivations and behavior, you have to ask yourself not just "what would I do in his circumstance?" but "how is he different from me and how does that difference impact what I'd do in his circumstance?"
A privilege is an advantage enjoyed by one group over another that is bestowed by the current configuration of society (and not by, say, biology or geography). Privilege between individuals is stochastically inherited from groups, and manifests itself in differences in evaluation of the same situation. It can be detected by modifying the golden rule from "Put yourself in their shoes" to "Put yourself in their shoes, then ask how they're different from you and how that difference would impact your response."