In short: Samsung was recently awarded a patent, published via the World Intellectual Property Organization (WIPO), that allows for control over the shape of a flexible display. Specifically, the patent (first applied for in 2015) applies to devices currently described as in-development which utilize a plastic film over an LCD panel which is easily folded or bent and a "shape maintaining part" held within a given device's body or frame. The entire device is set to be flexible as well and an electrical signal is sent to the shape maintaining part based on the "deformation state" of the display in order to help it maintain a predetermined shape. In effect, while the entire display would be "flexible" or foldable, the corresponding images show that it's primarily a portion of the device itself that is flexible and can essentially be locked into place. With that said, other associated images do seem to suggest there are many other ways this could be used with much more flexibility, such as in a rollable display.
Background: The South Korean tech giant has been patenting and teasing a foldable or even rollable smartphone for years at this point. However, it is slated to release its first generation of the former of those at some point in 2018, according to the company's mobile chief executive. What's more, there have also been some apparent leaks surrounding a few aspects of that device. For example, it's currently expected to feature a 4.6-inch rear panel display for use when folded and a tablet-sized 7.3-inch panel when folded out. Meanwhile, a curvature ratio of 1.5R is said to be accomplished using a Samsung-build OLED panel and the latest internal specs will be used – presumably similar to the Galaxy Note 9. Having said that, it's not necessarily likely that handset will be making use of this new technology in the patent. While that is entirely possible, the patent explicitly defines its display as being an LCD panel.
Impact: If the design works as advertised in the patent, at least one part of a problem intrinsic to the idea of a truly flexible display may finally be ready to be solved. Summarily, the company may have finally discovered a way to provide users with a completely flexible device without forcing them to deal with holding the ensuing fold at a position by themselves. Instead, the device will be able to determine the position of the fold and enact a locking mechanism to hold the device in its position. That would almost certainly make using such a device much easier and may additionally serve to improve the stability and durability as well. In the future, it's not difficult to imagine a similar technology might even make it possible for customers to choose the shape they want a foldable, rollable, or flexible smartphone to adopt while in use.