[0] Emergence, Coarse-graining, blah blah blah
(A quick foundational overview to make sure we're on the same page)
A gas is a human-scale object composed of many many individual micro-scale objects; I will call them atoms. A full description of the gas would be, say, the position and momentum of every atom within it. This would, roughly, comprise all of the information in the system, and would allow one to make perfect predictions about the future state of the gas. It would also be massive overkill. In systems of scale, the amount of information is far too much for a human to measure and memorize, let alone keep track of. Furthermore, the individual behavior of the atoms is extremely random, as they jiggle about and bump into each other, tending quickly toward collectively homogenous behavior. This is why we do not, in practice, describe gasses as lists of atom states. We prefer a higher-level, coarse-grained, fluid description, where we treat the gas as one object, smoothly distributed in space, with properties like temperature and pressure. Individual atoms do not have temperature and pressure, rather, these properties are useful descriptions of the atoms' collective behavior.
Human cultures/societies can be (and are) understood in a similar way. They are collective objects composed of many individual human agents, acting according to their own whims. An important difference is that the behavior of atoms is extremely simple: one or two equations, and you're done. Human agents, on the other hand, are very complicated and heterogeneous, each working on some extremely complex function of their memory and sense data. Modelling the complex interactions of simple parts is difficult enough, the complex interactions of complex parts is another thing entirely.
[1] Categorization
There are two human behaviors/properties which are important to this post.
1. Humans observe and model the world around them.
Notably, atoms do not do this. Their behavior is affected by their environment, but only in very simple ways (slide down potential gradients, and... that's it). Humans, on the other hand, are eager to build and store more nuanced understandings of the world around them, and those understandings meaningfully (and complicatedly) affect their behavior. This is often done through categorization systems. In an attempt to understand people, we mentally group them based on looks, behavior, etc. This way, we only need to understand the behavior of groups and classes of people, as opposed to each individual. This is similar to the coarse-grained model of gasses. Tracking the behavior of millions of individual parts is extremely impractical, hence why we have to create some higher-level collective description.
This applies not just to others, but also to oneself: Humans seek to understand themselves in terms of the higher-level, collective structure and categorizations. This manifests as the desire to identify oneself as part of a larger group.
But, as I've reiterated, people are extremely complex and heterogeneous. For this reason, our intuitive higher-level descriptions of collective human behavior tend to be of very low quality.
[2] Self-Organization
2. Humans actively fit their behavior to their models.
This one is more subtle. Not only do people categorize, but they also seek to enforce their categorizations, in both themselves and others. People insist that others update their behavior to fit their models, instead of updating the models to fit their behavior. More subtly, people modify their own behavior to fit their models as well. The Placebo effect is a straightforward example of this, but it's a very general phenomenon. Humans tend to fit their behavior (and state) to their own self-perception, consciously or otherwise.
Thus, we have a collective object (society, culture, etc) made up by individual elements (humans), where the behavior at one scale is (in a sense) influenced by the behavior at the other. Atoms do not analyze the collective state of a gas in order to decide their behavior, but humans do. The result is a strange feedback loop. In the case I've described, a positive one, tending toward stratification, I think. Humans try to model the state of their culture, and then enforce their model amongst themselves, which causes it to manifest. Through this process, even initially inaccurate categorization systems will tend to become accurate in time, according to their popularity. Not because the categorization evolves, but because the humans do.
The question of how a categorization system is poularized while also being inaccurate is another matter, though. A question of information dissemination, I think. Understanding that, alongside this principle, may be enough to get a very deep insight into how cultures and societies tend to structure themselves. At least, this is my working understanding.