1715, "style of dress," but also more broadly "custom or usage with respect to place and time, as represented in art or literature; distinctive action, appearance, arms, furniture, etc.," from French costume (17c.), from Italian costume "fashion, habit," from Latin consuetudinem (nominative consuetudo) "custom, habit, usage." Essentially the same word as custom but arriving by a different path.
It originally was an art term, referring to congruity in representation. From "customary clothes of the particular period in which the scene is laid," the meaning broadened by 1818 to "any defined mode of dress, external dress." Costume jewelry, made to be worn as an accessory to fashionable costume, is attested by 1917. Related: Costumic.
to dress, furnish with a costume," "1823, from costume (n.). Related: Costumed; costuming.