Eliezer's sequences touch upon this concept but I'm not sure they actually use the phrase. Much of my understanding of it came from in-person conversations. Various comments and posts have discussed it but to my knowledge there isn't a clear online writeup.
Social groups tend to coordinate around a shared set of beliefs. “Social reality” refers to either the world implied by this belief-set or the social process that produces it.
It can be confusing to talk about social reality because people engaging in this sort of coordination often find it much easier to treat social reality as reality than to track their own perspective and the shared perspective separately.
A great deal of my affection for hackers comes from the unique way they bridge the world of seeking secrets about people and secrets about the natural world. This might seem strange, since the stereotype is that hackers are lonely people that are alienated from others, but this is only half truth. In both the open source MIT tradition and the computer intrusion phone phreaking tradition, the search for secrets and excellence are paramount but fellow travelers are absolutely welcome on the journey. Further, much of even the ‘benign’ hacking tradition relies on the manipulation of social reality, the invisible relationships between people and symbols and things that are obvious to us but might confuse a visitor from Mars. For example, this story from the Jargon File about sneaking a computer into a hospital exemplifies the nature of social reality well. In Sister Y’s essay she hypothesizes that nerds are people who have a natural ability to see the underlying mechanisms of social reality in a way that is invisible to most people. Mostly through their natural inability to understand it in one way or another. Things that normal people take for granted confuse nerds, which provides the impetus for making discoveries about social reality itself.
A dictionary definition might be something like:
The map of the world which is drawn by our social-cultural universe, and its relationship to the standard protocols of societal interaction & cooperation. Implicit beliefs found in our norms & behavior toward others, as expressed through: coercive norms, rituals, rank, class, social status, authority, law, and other human coordination constructs.
One aspect of social reality is the offsets between our shared map and the territory. In many old African regional faiths, it was thought to be necessary for commoners to be kept away from upper class shamans and wizards. Otherwise their influence might damage their powers, or cause them to lose emotional control and damage the community. The idea that these people have magic powers and must be protected, along with the social norms and practices that arise from that is an example of social reality. It has very little to do with any real magic powers, but clearly there was some in-territory sequence of events that got everyone to decide to interpret the world this way.
This foreign, ancient example is useful because you have no emotional attachment to it, so you're in a position to evaluate it objectively. Ask yourself how people might react to a lower class person that insisted on touching the magic king. What about someone who refused to recant their belief that the magic king had no influence on the weather? As you imagine the reactions, consider what things in your own social sphere or society would be met with similar feelings from others. Then ask yourself if they're a human universal, or something that could theoretically be different if people felt differently. Once you've identified a handful of these you're on your way to examining social reality as a phenomena. I suggest you keep most of these thoughts to yourself, for your own protection.
Another aspect is the invisible models and expectations of others. In the Jargon File example above, the guard has been told that his role is to prevent unauthorized items from entering the building. This role is very much real, and its "procedures" are as rote and trickable as any computer program. As Morpheus tells us:
This is a sparring program, similar to the programmed reality of The Matrix. It has the same basic rules, rules like gravity. What you must learn is that these rules are no different than the rules of a computer system. Some of them can be bent. Others, can be broken.
A great deal of the phone phreaking tradition is about running a wedge into the places where social reality and the territory don't meet, and performing wild stunts based on them. For example, did you know that one of the most common attacks against locks is to just order a second lock because they're keyed-alike?
The big difference of course is that when you trick a computer program, it doesn't notice. Humans are very likely to notice you tricking them if you violate their expectations. So the art of social engineering is a very different realm in that respect, the technical complexity is lower but the solution space is narrowed by what people won't perceive as too strange. It engages your EQ, at least as much as it engages your IQ.
Some book recommendations for a better sense:
Ghost In The Wires by Kevin Mitnick
The Challenger Launch Decision by Diane Vaughan
The Righteous Mind by Jonathon Haidt
Here's how I use the terms "(natural) reality" and "social reality":
Natural reality is "that which doesn't go away if you stop believing in it" (P. K. Dick).
Social reality is that which doesn't go away when you alone stop believing in it, but it does go away proportionally to how many people stop believing in it (weighted, it seems, by something like "social belief negotiating power", or what pick-up artists would call "the strength of one's frame", I think). Example: "Bob is the highest-status person in this social group."
Why call it "reality"?
Eliezer said about reality in general: "I need different names for the thingies that determine my predictions and the thingy that determines my experimental results. I call the former thingies ‘belief’, and the latter thingy ‘reality’" (from The Simple Truth).
From your individual point of view, social reality behaves exactly like that—it is given; you are a price-taker; you can run experiments against it and it will determine the results.
The scope of what falls under natural reality, i.e. what doesn't go away when person X stops believing in it, is the same for every X; it is objective.
The funny thing about social reality is that it's not objective in this sense. For someone with a very strong frame, the scope of social reality (i.e. what doesn't go away when they stop believing in it, or more interestingly put, what doesn't materialize as soon as they start believing in it) is very small, and vice versa. ("Funny" mostly for the strong-frame people, because their life seems almost magically easier from the POV of someone who happens to have a combination of a much weaker frame and very low status. I assume it's not very funny for the latter person.)
Things can also fall in and out of the scope of your social reality (e.g. when you move to go to college, you can reinvent your social role, but then it slowly ossifies around you and becomes inescapable reality).
(I wanted to link Valentine Smith's post on the Intelligent Social Web as a more in-depth explanation, but I noticed you commented on it, so I could've saved myself the trouble and just said "yeah, that". Well, nevermind.)
I haven't yet fully checked whether I endorse the description there but it seemed good to link to Ruby's post:
Do you ever get the feeling that you're unsure what was true until the moment you said it? Like on the inside you're this highly contextual malleable thing but when you act it resolves and then you become consistent with something for a time?
Do you ever feel like you're writing checks you can't quite cash, running ahead, saying as true what you plan to *make* true, what becomes true in the saying it. Do you ever experience imposter syndrome?
Do you ever feel like we're all playing a game of pretend and nobody can quite step out of character?