Full Definition of FRANKINCENSE. : a fragrant gum resin from trees of a genus (Boswellia of the family Burseraceae) of Somalia and southern coastal Arabia that is an important incense resin and has been used in religious rites, perfumery, and embalming.See frankincense defined for English-language learners.See frankincense defined for kids.ADVERTISEMENT. a fragrant gum resin from trees of a genus (Boswellia of the family Burseraceae) of Somalia and southern coastal Arabia that is an important incense resin and has been used in religious rites, perfumery, and embalming. See frankincense defined for English-language learners. See frankincense defined for kids. ADVERTISEMENT.