Frankincense is the dried gum resin of trees in the genus Boswellia, principally Boswellia sacra in Oman and Yemen, Boswellia carterii in Somalia, and Boswellia papyrifera in Ethiopia and Sudan. The trees grow in arid limestone country that will support very little else, which is a large part of why the trade mattered so much: the resin was the only exportable wealth of the regions that produced it.
Harvesting is done by cutting the bark and letting the exuded resin harden into the pale lumps called tears, which are scraped off after a few weeks. A tree is tapped repeatedly through a season. The practice is old and it is not gentle; there is a documented modern problem of over-tapping suppressing seed production, and several Boswellia populations are in decline.
The English name has nothing to do with France or with any place. It comes from Old French franc encens, meaning free or pure incense, in the sense of high quality. The Latin is tus, the Greek libanos, and the Arabic luban, which is the word still used in Oman.
The resin contains boswellic acids, which have been the subject of a genuine and continuing body of pharmacological research into inflammation. That research is real; the conclusion is not yet settled, and no clinical claim should be read into the traditional use. What can be said without qualification is that the aromatic behaviour is a matter of volatile terpenes released on heating, which is why frankincense is burned rather than eaten.
Myrrh, its constant companion in the sources, is a different resin from a different genus, Commiphora, growing in the same regions. The two are routinely paired and are not the same substance: myrrh is bitter, darker, and was used in embalming and as a wound treatment, where frankincense was primarily burned.