Rigid Flex is more of a construction technique than an actual single material. As its name implies, "Rigid-Flex" is a composite of two different materials, one flexible, (such as Pyralux) and the other rigid (FR-4).
The applications for this type of board are practically unlimited, but its functionalities are especially useful for any application that requires connection to moving or bending parts and also requires a stable platform for components. Example applications include video cameras, laptops, or cellular phones. These consumer products have moving parts that bend of fold but are still connected to solid platform.