I wrote a couple posts on my personal blog a while ago about creativity. I was considering cross-posting them here but didn't think they were LessWrong-y enough. Quick summary: I think because of the one-way nature of most problems we face (it's easier to recognize a solution than it is to generate it), pretty much all of the problem solving we do is guess-and-check. That is, the brain kind of throws up solutions to problems blindly, and then we consciously check to see if the solutions are any good. So what we call "creativity" is just "those algorithms in the brain that suggest solutions to problems, but that we lack introspective access to". The lack of introspective access means it's difficult to pass creative skills on - think of a writer trying to explain how to write well. They can give a few basic rules of thumb, but most of their skill is contained within a black box that suggests possible sentences. The actual writing process is something like "wait for brain to come up with some candidate next sentence", and then "for each sentence, make a function call to 'is-sentence-good?' module of brain" (in other words, guess and check). Good writers/creative people are just those people who have brain algorithms that are unusually good at raising the correct solution to attention out of the vast possible space of solutions we could be considering. Of course, sometimes one has insights into a rule or process that generates some of the creative suggestions of the brain. When that happens you can verbalize explicitly how the creative skill works, and it stops being "creative" - you can just pass it on to anyone as a simple rule or procedure. This kind of maps nicely onto the art/science divide, as in "more of an art than a science". Skills are "arts" if they are non-proceduralizable because the algorithms that generate the skill are immune to introspection, and skills are "sciences" if the algorithms have been "brought up into consciousness", so to speak, to the point where they can be explicitly described and shared (of course, I think art vs science is a terrible way to describe this dichotomy, because science is probably the most creative, least proceduralizable thing we do, but what are you gonna do?)

Anyway, I don't know if all of this is just already obvious to everyone here, but I've found it a very useful way to think about creativity.

Edit: I missed your last sentence somehow. The above is definitely just plausible and/or fun to read.