An operator was any individual who operated a specific piece of equipment or console. Transporter rooms aboard Federation starships were manned by transporter operators.
When the USS Enterprise-D intercepted the Erstwhile in 2365, its pilot, Thadiun Okona, upon being hailed, identified himself as "the owner and operator of this craft". (TNG: "The Outrageous Okona")
Quark saw himself, through the eyes of his peers – Ferengi businessmen – to be "a second-rate, small-time operator." (DS9: "Body Parts")
During their brief employment at the Central Power Facility on Quarra in 2377, the facility's efficiency moniter (and former USS Voyager crewmember) Annika Hansen confronted (former Voyager captain) Kathryn Janeway and Jaffen while they were "fraternizing" at Janeway's station. Seven attempted to break up there mingling by informing them that "[Janeway's] station doesn't require two operators." (VOY: "Workforce")
In 2378, an EMH miner, stationed at a dilithium processing facility, instructed a second EMH miner to report to the holo-lab, adding that he ask the operator to run program 47-Beta. (VOY: "Author, Author")