Traditionally. a fake book is a book, usually compiled by a musician for his own use, that contains a whole bunch of songs and just enough information about how to play each song (a few chords, some notation, whatever) to allow the musician to "fake" it if the song is requested. In the old days "faking it" meant playing a song that you really don't know how to play, and for which you don't have the sheet music, but coming close enough to be recognizable and to satisfy the audience