There do exist dedicated transcription services and solutions, for example VoiceBase or Translator Professional that can transform the speech from an audio (such as .aiff) and save the words in a textual format (.txt mostly) It may not always be perfect and commonly requires manual editing done by human.
Found 2 different conversion types using the same filename extensions.
Conversion aiff to txt type 1:
Convert from Audio Interchange File Format to Simple text file.
On-line services software - convert aiff to txt on web
A Voice Search & Transcription Platform
File type (from-> to)
Convert from aiff file format
Audio Interchange File Format
Simple text file
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned aiff to txt. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Conversion aiff to txt type 2:
Convert from Audio Interchange File Format to Steinberg LM-4 bank file.
Multiplatform software - convert aiff to txt on any platform
A professional instrument conversion program