Creating notation for a piece of music based on a performance recording. This can also refer to rewriting music for a different instrumentation than what was originally intended.
Transcription is the process of writing down music by identifying aurally the notes and gestures being played. It is a useful exercise for ear training, and is also commonly used by jazz musicians to learn improvised solos that may never have been previously notated.
Another use of the term refers to rewriting a piece of music, either solo or ensemble, for another instrument or other instruments than which it was originally intended.
The term "arrangement" is somewhat interchangeable with this usage, although transcriptions are always faithful adaptations, whereas arrangements can change significant aspects of the original piece.