"jazz cigarette" means: A euphemistic and often humorous British slang term for a cannabis cigarette — a joint or spliff. The name evokes the association between ja.... There is a drug-related reference, so this is one worth noticing without overreacting. Many teens encounter such vocabulary through music, film and friends without any direct involvement. A neutral, curious conversation about where they heard the term and what they understand by it is far more useful than a confrontation. Watch for repeated context, not a single word.