I have read (and heard) answers to this question many times, but the most common answer, and the one given by the programme makers was that it didn't actually stand for anything it just sounded good and the sort of thing that members of IR would say!
'Fab' was a word in common use at the time [The Beatles were the 'Fab Four'] and the makers of the programme simply turned the letters into what sounded like an acronym, but which was in reality meaningless.
I find it somewhat hard to believe that there is no actual meaning for F.A.B? especially when you take into account other Gerry Anderson productions that had similar acronyms... for instance On Captain Scarlet it was S.I.G or "Spectrum Is Green" and on Terra Hawks the used the CB radio type codes (IE 10-10, 10-15) I'm pretty sure that other shows like Stingray, UFO, Space 1999 and Space Precinct also used similar code abreviations as well :)