Definition and background:
the stated (but unreachable) goal of performing a piece in the way it would have originally sounded or in the way the composer intended for it to sound. A less contentious term is "historically informed." See performance practice.
For more information on the music term "Authenticity" check out these other resources:
Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary