mid-15c., "short garment for men," from Old French jaquet "short coat with sleeves," diminutive of jaque, a kind of tunic, which is of uncertain origin. Probably it is from Jacque, the male proper name, also the generic name of a French peasant (see jacquerie) with extended material senses as in native jack (n.). But possibly it is from or influenced by jaque (de mailles) "short, tight-fitting coat," originally "coat of mail," from Spanish jaco, from Arabic shakk "breastplate." Meaning "paper wrapper of a book" is first attested 1886.
Iakke, jakke "a short, close-fitting stuffed or quilted tunic, often serving as a defensive garment" is attested in English from late 14c. (from Old French jaque), and by c. 1400 was being used for "woman's short tunic." It is possible that jacket was formed in English as a diminutive of this.