Some good answers most of which are valid. I'll post my top reasons. My knowledge is based from my company, Harvest Cellular that buys back broken LCD screens here in the USA and sells this product back to the refurbish companies so I'm dealing with China a lot and the conversation comes up often when chatting with our clients.
In my eyes, there are two main influences
1) External Supply / Demand
A) Official Channels - The big carriers and prepaid guys are starting to sell iPhones as a loss-leader to acquire customers. Official channels push them as over the counter exchanges and Apple's new lower prices warranty options has all of these guys needing more and more refurbished phones. Instead of them being turned back into an LCD screen part to be sold to consumers or repair shops, their going directly back onto devices.
B) Red Haze - 5/5c/5s LCD screens were plagued with a red haze tint that appears after several months of usage. This is around 40%. Consumers and repair shops consider this inferior and while some slip them into orders to average down or sell for less, the simple economics of not having ~40% of goods to reclaim has created a shortage. Now, people are getting less picky and accepting these types.
2) Current Events
A) New iPhone - When the new iphone 6s and 6s+ came out, it seemed to get worse. Both customs here in the USA and the HK to China underground seemed to step up seizures. Same as Apple did two years ago by pulling the plug on iPhone unlocks during the release of 5s/5c. Temporary, this creates a shortage of used LCD screens and devices and surely has many going to upgrade or buy the new things.
B) Shortage of Parts - Parts like the film for the back light were in shortage as well as OEM IC chips. There isn't 1,000 factories making this stuff in China. More like a handful account for a majority (80%+) of the production. I think it's obvious without these "little parts" you can't complete production.
I think all of these and more influence the current past and current situation and all just fell in place at the same time. On a side note, I really think 1A above is really playing a powerful role and will continue. The cost and value of 2nd hand devices are now within reason and available after so many people upgrade after 10 months compared to several years ago.
Likewise, I agree with Atronix that Apple wants a piece of 2nd hand market; repairs and phone buybacks. While they may not do it directly their ability to offer the service with partners, they're slowly entering the space enough to influence the grey market. Cell phone repair went from 1B to 2B annually in just a few years and I'm sure this didn't elude them.