The classic definition of a "drone" involves several aspects including (1) Male honeybees which gather no honey; (2) One who lives on the labors of others; a lazy, idle fellow; and (3) That which gives out a monotonous tone or dull sound. Leave it to the worker bees to come up with a term called "office drone." It is a nickname given to the laziest person in the cube farm, or the one who tries to pass off as much work as possible while still maintaining the semblance of productivity (see also: throw it over the wall).
In other words, if your life resembles a Dilbert character, your colleagues may be secretly calling you the office drone behind your back. However most office drones are keenly aware of their sluggardness and openly acknowledge it, for example "As the token office drone, I am constantly looking for ways I can break free of the monotonous, death pit of Entry-Level Temp Work."