Definition and background:
The diameter of the tube of a woodwind or brass instrument. The shape of the bore in part dictitates the timbre or tone color of the instrument. A conical bore instrument, in which the bore grows larger throughout, such as the cornet, produces a mellow timbre while a cylindrical bore instrument, such as the trumpet, which has a constant bore until the flare of the bell, produces a brighter, more brilliant timbre.
For more information on the music term "Bore" check out these other resources:
Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary