A Cifi unit was an electronic microchip connected to an ansible that provided instantaneous communication with the desired individual. Usually worn in one's ear, the implant looked like a purple jewel. Andrew Wiggin, Peter Wiggin II, and Miro Ribeira wore one in order to have constant communication with Jane.
The implants were commonplace on various worlds, but were considered unnatural or disrespectful to some.
The word "cifi unit" was possibly a phoneticized acronym for "Cochlear Implanted Philotic Interface". The 'ph' probably replaced with 'f' as a simplification over many centuries of use among the Hundred Worlds.