Operate = (1) direct or control something: Do you know how to operate this machinery? (2) perform surgery on (medicine): Have you heard what happened to the last patient he operated on? (3) to perform a function or work: The motor operates smoothly.The camera also operates underwater. (4) to be involved in military activities: A militant group is operating against the government.
Operation = (1) the state of being in effect or being operative: That law is no longer in operation. (2) a planned activity involving many people performing various actions: They planned a rescue operation. (3) a medical procedure involving an incision with instruments: My mother is having an operation tomorrow. Mr. Barrett is going to have an operation on his back.