In academia, adding the prefix "post" to a movement, theory, or genre is quite common. The best way to describe the meaning of "post" in this context is as a synonym for "beyond", building on the innovations, theories, or style of the original in such a way as to take it beyond what the original was, in the process creating a new theory, genre, or whatever. In other words, the only way to define something is to describe what it evolved from. See also Evolving Trope.
However, pop culture doesn't think very highly of this use of "post", hence the rather flippant term "post-somethingism" that lends itself to the trope name. The belief here is that such concepts are ill-defined (if not a word seeking a definition) and a way for the pretentious "intelligentsia" to show how they've transcended whatever it is we're used to, so they don't have to follow any rules. Pop culture may or may not be right in its assessment, but more often than not, it amounts to creating a strawman of a genuine concept.
- Postmodernism is, in some sense, the Trope Codifier — hard to define, harder to understand, and commonly believed to be popular among people who believe True Art Is Incomprehensible and want to be seen as geniuses without anyone checking their work. The term really refers to a number of loosely connected movements with the common goal of rejecting the 1930s-era theory of modernism — that society and art were constantly moving in a positive direction toward a single overarching narrative. Put another way, a common definition used by postmodernists is that postmodernism is "an interruption of the modern mythological form". Postmodernism originated in part out of a perception that such modernist ideas were a major catalyst for World War II, but in the decades since, its definition has expanded and shifted so far that in some cases, it really is most accurate to define it as an excuse to not follow any rules. This in turn led to the logical endpoint of the movement — the creation of "post-postmodernism", rejecting postmodernism the way the latter rejected modernism.
- Post-Impressionism is the Ur-Example — it's a term coined by art historians to describe artists like Vincent van Gogh, Henri de Toulouse-Lautrec, or Paul Gauguin, who built on the innovations of the Impressionists but created new and different styles of expression. In its time, it was never a cohesive art movement so much as a bunch of loosely affiliated, like-minded, yet fiercely independent artists.
- Poststructuralism is the rejection of structuralism, a broad theory (but usually applied to literature) of strictly defined cultural archetypes and binaries — think The Hero with a Thousand Faces. Poststructuralist literary theory critiques and ultimately rejects such binary concepts as good versus evil and red versus blue, and indeed it can be expanded to rejection of wide-ranging social phenomena outside of literature like binary gender. There's a sociopolitical angle, too — many of these archetypes are seen as imposed by one culture on another through colonialism and oppression. The exact nature of poststructuralism changes rapidly; one decade TV Tropes itself would be "structuralist" because everything fits into a neat (albeit absurdly expansive) directory of tropes, but another decade it would be "poststructuralist" because there are so many different variations of the same trope that everything can only truly be defined as its own thing.
- "Post-genre" is common in popular music, usually as a reinvention of a genre in a more experimental direction. The most famous examples are Post-Punk, Post-Rock, and Post-Metal, but there are a few outliers that don't quite fit the pattern:
- Post-Grunge was the opposite phenomenon — grunge was always experimental, and "post-grunge" moved it in a more mainstream direction. The likely catalyst was Kurt Cobain's suicide in 1994, which left many audiences feeling disillusioned by traditional grunge's dark subject matter. The genre stagnated quickly, and by The New '10s it was essentially Condemned by History.
- Post-disco was a response to the incredible backlash against disco of the early 1980s. It similarly brought the genre more "mainstream", stripping away the funk elements and introducing dub and R&B. The result had a significant impact on pop that's still felt today.
- Post-Britpop was a response to the genre's inability to break out of Britain into America, which contributed to its collapse by the late 1990s. It removed overtly British subject matter and replaced it with American indie rock. It was also more experimental, replacing an ill-defined genre with something even more nebulous.
- Post-Cyberpunk is an attempt to move beyond the cynicism and hopelessness of the Cyberpunk genre by showing a more optimistic future enabled by technology. Again, defining the genre by what it's not leads to a greater spectrum of works, but one common thread is that while technology does pose a threat, it can be used against itself (e.g. The Matrix, which notably does it with a Messianic Archetype). In other cases, Cyberpunk tropes are thoroughly deconstructed (e.g. Snow Crash, Transmetropolitan.
- Reconstruction follows similar logic despite not following the naming pattern — if it did one could call it "post-deconstruction". If deconstruction is a way of lobbying criticism at a genre, reconstruction isn't a rejection of the criticism but a means of moving beyond it, accepting it, and using the trappings of the genre more intelligently.
- Post-industrialism is a concept in economics which is actually fairly simple to grasp — in decades past, industrialization and manufacturing was the way to become a strong economy, but since then nations have found ways to become economic powerhouses with minimal industrial output by focusing on the service and finance sectors.
- Post-scarcity is similarly an economic concept — "scarcity" here refers to the possibility of the supply of goods running out (thus making them more expensive), whereas "post-scarcity" refers to goods whose supply cannot run out and the effect it has on its price. A good example is computer software; once it's written, it can be duplicated indefinitely at virtually no cost, and the only reason you have to pay for it is copyright.
- Post-colonialism is a more contentious example, in the sense that it seems to have taken on two distinct meanings that are only tangentially related. The first simply refers to the state of the world after the "golden age of colonialism" (i.e. after World War I), which saw huge global empires break up and countries having to flex their "soft power". The second refers to the sociological and economic ideologies and analyses that first emerged in the mid-20th century looking back on colonialism, this time not focused on how countries maintain power as much as people starting to ask how they got it in the first place. As such, this second strain is often highly critical of colonialism and Occidentalism for the suppression (and in some cases total erasure) of cultures outside their sphere.
- "Post-truth" is a tongue-in-cheek use of the trope to refer to the philosophy of not needing facts anymore. Although first coined in 1992, it catapulted into mainstream usage right around 2016, the year of the Brexit referendum and the election of Donald Trump, an era when "fake news" and "alternative facts" abounded on the Internet. Although often thought of as an indictment of the degradation of society into a credulous and fragile mindset, used more seriously, it's an indictment of the way the Internet works and affords people a way to pretend that the Blatant Lies that have existed throughout history aren't lies at all.