Personally, I've always defined it as the ability to take two separate ideas and create a third one.
The more creative people are, the more they have the ability to make a connection between two less related items.
I've often noticed the main difference between creative people and not so creative people isn't skill or intelligence or anything. Its the ability to not get phased by when you can't get an idea to work, you just keep plugging on like a small form of insanity even though you fail and fail. A biochemistry driven insanity I would say, I feed off the process of failing, and get massive elation when something that shouldn't work does work. To me failing is as important as succeeding, but the reward of succeeding is so much better.
And like most things, people rarely see the long chain of failures, so assume a brilliance to what might be better classed as a madness ;)
Creativity is the process of having original thought.
The oft debated aspect of that definition is whether original thought is valuable from a social standpoint, or that it's enough for original thought to merely have value for the individual.
But that's the most concise definition of creativity you'll ever get IMO.
I think creativity (humor/play/music) involves a context switch.
Like with comedy: the comedian sets up an expectation, then surprises the audience with a punchline which forces them to reinterpret the setup. And with music: the composer sets up a theme, and then repeats it slightly differently to keep the song interesting. The textbook example is Beethoven's 5th.
I think pg believes similarly. He said "creativity comes from functions applying to arguments of the wrong type" [1]. He also said "good design is slightly funny" [2].
