the purpose of a TFI module is to control the spark output of the ignition system. A signal is sent from the TFI to the ECU, where the ECU processes the received signal and correspondingly outputs the correct spark control for engine timing (advance/retard).
TFI stands for thick film ignition, or thick film integrated ignition (TFI-IV, in conjunction with EEC-IV). It is a small grey plastic module that houses solid-state electronic parts, all of which are suspended in a thick translucent, electrolytic (meaning it is conductive) film. The Thick Film Integrated Ignition (TFI-IV) name is proprietary to Ford. Others may know it referred to as a "spark module."
Back when Ford was using their EEC-IV engine control unit, it was coupled with a special ‘TFI’ module designed to control spark output via information attained from the EEC-IV control unit. Ford implemented this system in pretty much all of their production cars ranging from 1983-1995. For the Mustang, EEC-IV was introduced in 1984 and was used all the way up until the 1995 model (actual usage in Mustangs was from 1984-1994, so 10 years).