In other words, you can use "structural" to mean just about anything you want, as long as you're talking about a complex system. Here are some examples of how people in different walks of life use the word "structural":
1. "Structural estimation"
Econometricians sometimes use a technique known as "structural estimation." This term is usually used in contrast to "reduced-form estimation." It's very difficult to pin down exact definitions of "structural" and "reduced-form" - even economists often don't know where the boundary lies. In general, "reduced-form" models tend to be either linear, or simple stuff like probit or logit. "Structural" models tend to use more complicated functional forms that represent "underlying" economic relationships. The implication of using a "structural" model is that your model can describe a wider array of situations, but this is just sort of implied. "Reduced-form" is often used as a diss, but that's not always fair - after all, if the assumptions that make your model "structural" are wrong, your model will give you a false sense of confidence.
2. "Structural Poverty"
Advocates for the poor usually don't like the idea that poor people could be non-poor if they altered their behavior. They claim that poverty is the unavoidable result of the way the economy, society, and politics are set up. Being screwed by the system is what they label "structural poverty".
3. "Structural VARs"
In time-series econometrics, you have "reduced-form vector autoregressions," in which the shocks (random stuff) are things you can observe. Unfortunately, because you can observe anything you like and call it a "shock", the shocks in your VAR model will inevitably be correlated, which limits the applicability of the model. So if you want a VAR that will work in all cases - or at least, a much wider set of cases - you need to estimate the "structural" shocks. Since you can't observe these. you have to make some assumptions about how they interact to form the reduced-form shocks.
4. "Structural Deficits"
This refers to government deficits that are unrelated to the business cycle. It is a term used by deficit hawks to mean a deficit that is very dangerous, because it will just keep getting larger unless there are major political changes. A related concept is structural unemployment, which is unemployment that doesn't change with the business cycle.
5. "Deep Structural Parameters"
This is a word that economists use to mean things that don't change in response to economic policy. For example, followers of Robert Lucas often argue that preferences and technology don't respond when policy changes, and should thus be treated as "deep structural" parameters in economic models. In practice, anything will probably change at least a tiny bit in response to some kind of policy, so the assumption of "deep structuralness" will always be an approximation.
6. "Structural Pluralism"
This is...OK, I don't understand what this is. It's a term used by sociologists. According to this article, "Structural pluralism is defined as the degree of differentiation in the social system along institutional and specialized interest group lines, in a way that determines the potential sources of organized social power." I think that means that when a society has different types of organizations - e.g. religions, unions, corporations, etc. - that all have some sort of influence, you have structural pluralism. But I'm not sure.
7. "Structural Integration"
This is a kooky-sounding type of physical therapy. But it might work!
8. "Structural Assimilation"
This is when minorities have equal access to public institutions. How this could be observed and verified in practice, I'm not sure...maybe you could use a structural model.
9. "Structural Racism"
This is when "dynamics" exist that discriminate against minorities. For the meaning of "dynamics," you will have to wait for a different blog post.
10. "Structural Realism"
This is a philosophy, possibly part of epistemology or possibly part of ontology (I'm never sure where one ends and the other begins), that, according to the Stanford Encyclopedia of Philosophy, "is considered by many realists and antirealists alike as the most defensible form of scientific realism." Further down in the article, we learn that "Structural realism is often characterised as the view that scientific theories tell us only about the form or structure of the unobservable world and not about its nature." Basically, it seems to mean that there's stuff we can't totally know about, but that science can let us know some stuff about that stuff.
So what does "structural" really mean? Looking at all these examples, it seems to mean "stuff I can't directly show you, but which I'm pretty sure isn't going to go away or change any time soon." So basically, "structural" = "stable" + "unobservable". Structure is the man behind the curtain. Does that sound right?
Except for structural integration, of course. I don't know how to fit that one in.