Definition and background:
Short for ad libitum.A term used in jazz music as a slang for an improvised solo, or a solo performed without written notation, but where the performer improvises a melody based around the melodic and harmonic structure of the original melody.
For more information on the music term "Ad lib" check out these other resources:
Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary