I can't define what "post-modernism" is, however I realized that I can try to describe it, that is, describe life and trends of post-modern world.
Music of post-modern world is music without meaning, which means usually without words at all. It can be said about art probably too.
Movies of post-modern world are mostly fantasy and futuristic action movies. Movies about existing reality and present times and present problems are not popular.
Virtual Reality will become more and more popular for the same reasons as fantasy movies.
No dream. John Lennon famously sang "The dream is over". That might be true in the context of individual but it's also true in the context of society. Society in the post-modern world has no shared communal dream (myth, narrative).
Political discourse either doesn't exist or exist in the form of the comedy. The most popular and famous political critics are comedians. This trend is true for various countries, from USA to Ukraine.
Trivialization of everything: politics, environment, sex, media.
HyperNormalization - majority people have same clothing (few brands and few styles), same phone (two providers), listen to the same music (few artists), watch same movies (made in the same place), have same opinions by there own choise. Adam Curtius made a great documentary about this topic.
Facelessness - belief that everything is run by systems, not humans. E.g. market, or EU establishment, corporations - it's believed that there are no people behind it.
The rise of profanity. It's in media, television, offices, streets.
Growing inequality - rich people getting richer across different countries from USA to Brazil.
No alternative - general belief in the existing system, understanding it's flaws but refusal to believe in any alternatives. There is some belief that life is still getting better and that there is still some progress (at least small one). We an example have wishfull thinking here on the global scale.
Abundance of information - everyone can access information on the very complicated matters almost instantly. However, that changes nothing. Knowledge and wisdom is still as inaccessible as they were. All the available information provides no tips, no hope, no ideas.
Communal schizophrenia, by this I mean that we live in a world that doesn't seem real, but more like "Alice in Wonderland". E.g. chritistian conservative parties promote anti-Christian values, liberal politicians deploy drone attacks. Laws and legal acts get beautiful names that actually do opposite thing.
Continuing globalization - archetypes of issues and politicians that we have in one country are very similar to the other countries.
Unseriousness - people are not keen to talk on serious topics in larger groups (either politics, mental health or other topic). You are supposed to look happy and talk on fun topics in a group. When serious discussion, unpleasant news are brought up in a group - people look scared.
Aging - aging seems like a scary thing for a lot of people. They will continue search for looking younger. 20-35 years range is where majority of population is trying to visually remain as long as possible.
Growing conservatism on both right and left, and general tendency for even bigger consolidation of right and left.
Protest becoming more commoditized. It's more about symbols and merchandise (t-shirts, hats etc) than substance and content.