In short: we don't know.
But... we are learning. Most recently, Jonah Lehrer released his latest book, Imagine - How Creativity Works. The book has become a massive bestseller and, just this week, it was announced that Lehrer is leaving his regular post at Wired Magazine to join The New Yorker (more on that here: Jonah Lehrer Departs Wired for The New Yorker). Imagine is a fascinating journey that looks at everything from the biology behind creativity to where ideas come from. Lehrer recently spoke to the staff at Google about his latest book and his findings behind the mystery that is creativity.
Here's one great hour on the topic of creativity with Jonah Lehrer: