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Like a reed in the wind (or a hero in a kung fu movie) perhaps it can bend, and not break. This could be very nice on devices that tend to get dropped occasionally...such as the ones I own. Other than that, perhaps it could be useful in wearable devices such as smart watches. With a lot of smart people thinking about ways to utilize the technology, I’m sure some interesting uses will soon be explored.
It's a good question. This article quotes a Samsung executive who says flexible form factors "will really begin to change how people interact with their devices, opening up new lifestyle possibilities ... [and] allow our partners to create a whole new ecosystem of devices." But there are no specific examples offered in the article, other than a prototype phone with a screen that extends to the sides of the device, allowing users to read messages. I expect there will be some cool uses for flexible screens not far down the road.