The LG G Flex has a curved six inch display that is curved along its length to fit the palm of your hand and the shape of your face. The OLED plastic display can actually be pressed down flat onto a table and then move back into its curved shape, but it really isn't designed for you to flex it constantly.
In addition to the flexible display, the back has a self-healing coating that is designed to help reduce the effects of daily wear and tear. Like the LG G2, there are also rear controls for power and volume.
The LG G Flex has a 2.26 GHz quad-core Snapdragon 800 processor, 13 megapixel camera, 3,500 mAh battery (it is curved as well), and LG features such as KnockON, Slide Aside, Qslide, and Dual Window. I understand the curved display is also designed to provide an optimized video experience.
The LG G Flex should be available in the first quarter of 2014, but no pricing information has yet been made available.