Projected File System aka ProjFS is a feature similar to FUSE found on Linux (or to Dokan & WinFSP). It allows apps to create virtual file systems which appear indistinguishable from local folders, but their entire contents are generated "live" by the program. (In other words, you're seeing projections of files which might not be there.)
The primary use of ProjFS is Microsoft's "Git Virtual File System", an addon to the Git version management tool aimed at increasing its performance and reducing disk space usage when dealing with massive repositories. (Git was built for repositories containing just tens of thousands of files, such as Linux.git; but Microsoft have started using it internally for the Windows source repository, which is several orders of magnitude larger.)
Additionally, Visual Studio (Enterprise)'s "Live Unit Testing" feature requires ProjFS to be enabled
Currently ProjFS doesn't seem to be publicly documented, but I expect that sooner or later third-party developers will figure out how to use it as a FUSE alternative for implementing such virtual filesystems as sshfs, ftpfs, and so on.
Note: Projected File System has nothing to do with Windows File Protection.
As noted in the comments, documentation is now available for the feature.