late 14c., "action, performance, work," also "the performance of some science or art," from Old French operacion "operation, working, proceedings," from Latin operationem (nominative operatio) "a working, operation," noun of action from past-participle stem of operari "to work, labor" (in Late Latin "to have effect, be active, cause"), from opera "work, effort," related to opus (genitive operis) "a work" (from PIE root *op- "to work, produce in abundance").
The surgical sense of "act or series of acts performed upon a patient's body," usually with instruments, is first attested 1590s. The military sense of "act of carrying out a preconcerted series of movements" is by 1749.
late 15c., operatif, "active, working," from Old French operatif (14c.) and directly from Medieval Latin operativus "creative, formative," from operat-, past-participle stem of operari (see operation). Meaning "producing the intended effect" is from 1590s.
c. 1600, "to be in effect, perform or be at work, exert force or influence," a back-formation from operation (q.v.), or else from Latin operatus, past participle of operari "to work, labor, toil, take pains" (in Late Latin "to have effect, be active, cause"). The surgical sense of "perform some manual act upon the body of a patient," usually with instruments, is attested from 1799. Meaning "to work machinery" is from 1864 in American English. Related: Operated; operating. Operating system in the computer sense is from 1961.
"the operation or practice of fixing colors in solution in textiles, hides, hair, etc.," late 14c., verbal noun from dye (v.).