This is how it was explained to me when I joined ATC over 35 years ago.
A bandbox is a 17th century word given to a light cylindrical box used by military officers, clergymen and the aristocracy for storing their ruffs (then known as bands) collars, caps etc.
Over the years it has also come to mean to tidy things away i.e. put them in a bandbox.
In the 1960s many of the senior controllers were ex-RAF officers and the term "bandbox" was coined to indicate collapsing sectors onto one position or tidying up as you might say. The fact that radar consoles at the time were circular made it look as though all the sectors had been put into a bandbox.
