Face Library is probably the name of the library used for Nintendo games to be able to use Miis. The Wii's library is named RFL, which would stand for "Revolution Face Library".
There are libraries made for Wii (RFL), DS (NFL, only used by Tomodachi Life and Personal Trainer: Walking), 3DS (CFL), Wii U (FFL), mobile devices (Android and iOS) and the Switch. The Switch doesn't have proper Face Library, but some people might call it NXFL.
Nintendo put some restrictions to what the Face Library can be used for.