Like when you buy a new catcher's mit, or car, you're supposed to "break it in", like get it ready for action by actually using it. Burn in is the same thing, but for headphones.
This is the GREAT DEBATE here on Head-Fi aertus. Some will tell you that headphones won't sound good unless you burn them in (aka hook 'em up to a music source and just let them sit there) for HOURS on end. Some say like 20 hours is enough. Others say 200 is their minimum before they generally hear a difference in quality. The other "side" of the argument will say that's all fantasy and the REAL reason why headphones sound better after being "burned in" is because what actually happens is your brain/ears start to "get used" to the sound signature of your headphones, and it has nothing to do with burning it in.
Though in my OP I stated I gave my Cs' about 24 hours of burn in time before starting the review, I'm now at a point where I no longer plan to do burn-in. I'm starting to agree more with the side that says it's just a matter of your ears actually getting used to the sound and nothing at all to do with how much burn in time you put in.
Hope that helps!