Backend Interface (BKI) files are scripts in a special language that is understood by the PostgreSQL backend when running in the "bootstrap" mode. The bootstrap mode allows system catalogs to be created and filled from scratch, whereas ordinary SQL commands require the catalogs to exist already. BKI files can therefore be used to create the database system in the first place. (And they are probably not useful for anything else.)
initdb uses a BKI file to do part of its job when creating a new database cluster. The input file used by initdb is created as part of building and installing PostgreSQL by a program named genbki.sh, which reads some specially formatted C header files in the src/include/catalog/ directory of the source tree. The created BKI file is called postgres.bki and is normally installed in the share subdirectory of the installation tree.
Related information can be found in the documentation for initdb.