Origins
The word 'genius' has undergone one of the most dramatic transformations in the history of English: from a divine spirit to a human quality. In its original Latin sense, a 'genius' was not a person but a supernatural being — a guardian spirit born alongside every Roman male (the female equivalent was called 'juno') that embodied his productive and creative power, his essential nature, his vitality. The genius was not something you possessed; it was something that possessed you. When a Roman swore 'per genium meum' (by my genius), he was swearing by his attendant spirit.
The Latin word comes from 'gignere' (to beget, to produce, to bring forth), from PIE *ǵenh₁- (to give birth, to produce), one of the most productive roots in the Indo-European family. Through Latin alone, it produced: 'generate' (to bring forth), 'genesis' (origin, birth), 'gene' and 'genetic' (pertaining to birth and heredity), 'gender' (kind, type — originally 'birth-class'), 'genre' (kind, type), 'gentle' (well-born), 'generous' (of noble birth, then 'giving freely'), 'genuine' (native, natural, authentic), 'congenital' (born with), 'engine' (from 'ingenium,' inborn talent, then 'a clever device'), 'ingenious' (having inborn talent), and 'progenitor' (one who begets before). Through Germanic descendants of *ǵenh₁-, the root produced 'kin' (relatives, those born together), 'kind' (nature, type — originally 'birth-group'), 'king' (possibly 'son of the kin,' the one born to rule), and 'kindergarten' (children's garden).
The transformation from spirit to quality began in the Renaissance, when Latin 'genius' was increasingly used to mean 'natural disposition' or 'innate character' rather than 'guardian spirit.' By the seventeenth century, English 'genius' could mean 'a person's characteristic inclination or talent.' The final shift — from 'innate talent' to 'extraordinary, world-class intellectual power' — was largely an eighteenth-century development, influenced by discussions of artistic originality by writers like Edward Young ('Conjectures on Original Composition,' 1759) and later by Kant's analysis of genius in the 'Critique of Judgment' (1790), where he defined genius as 'the talent (natural endowment) which gives the rule to art.'
Latin Roots
The Arabic word 'jinn' (جن, a supernatural spirit) is not etymologically related to Latin 'genius,' but the two words influenced each other in European transmission. When Arabic texts were translated into Latin during the Middle Ages, translators sometimes rendered 'jinn' as 'genius' (or the French form 'génie'), blending the two concepts. The 'genie' of the lamp in 'Aladdin' (from the 'One Thousand and One Nights') is an Arabic jinn rendered through the French 'génie' — a convergence of two unrelated spirit-words that happened to sound similar.
Elizabeth Gilbert, in her 2009 TED talk, argued for recovering the original Roman meaning: instead of saying a person 'is a genius' (which creates crushing pressure), we should say a person 'has a genius' — a creative spirit that visits and sometimes departs. Whether or not one accepts the theology, the etymology supports her point: for most of its history, genius was something that came to you, not something you were.