Apple's foldable display patent describes how the display could fold outward, allowing both halves of the screen to remain accessible when the phone is closed shut. The two sides would connect via a clamshell-like hinge that allows them to rotate relative to each other, while flexible printed circuit boards keep the connection intact.
The gif in the OP seems cool. Like you'd have a phone sized device but it could easily become tablet sized when needed. I think that would be a cool thing to have access to. It would be especially helpful for watching videos.