The operator only appears in the episode, "Lost in Bikini Bottom." The operator is only heard speaking through the payphone as it is an automated message.
Role in episode
When SpongeBob, through a nearby payphone, attempts to ask Squidward what he should do since he was lost and surrounded by fire hydrants, the operator asks SpongeBob, through an automated message, to insert another dime to resume the call. SpongeBob states that he does not have another dime and asks the operator to to tell SpongeBob where he is. The operator then tells SpongeBob to insert another dime if he wishes to know where he is.