In interviews various famous and financially successful people from Alan Moore to Frank Zappa have replied "How the hell should I know?" Usually with the gist that their focus is on technique, rather than inspiration.
For instance, in "Drawing on the Right Side of the Brain", Betty Edwards insists that the right side, the non-linguistic section of the brain, is the source for human creativity, and being non-verbal, the process implicitly defies explanation.
Then there's the notion that ideas come from someplace else entirely.
Stephen King in his book "Stephen King on Writing" makes mention of a muse ( perhaps tongue in cheek) as a cigar chomping man who lives in a basement with a bag of magic which he shares only if he feels like it.
Keith Johnstone, the Improvisational Theater scholar suggests, in his book, "Impro". that ideas come from "someplace else" (or at the very least, not the ego), and later in his book "Impro for Storytellers" mentions "the Great Moose" as the source-god of Improv.
However, the human body is a conductor for transformational energy (ethereal as that sounds): much like our gastrointestinal systems turn Captain Crunch into excrement, our minds might digest raw material( sensory input, other concepts and influences) into a pile of steamy, warm, new ideas.
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But between theories of Moose Gods and Brain Poop I'll have to go with the former, jus' cause it's less gross.