In complex machinery the wheels that are apparently doing the work are turned by other, less obvious wheels. Figuratively, ‘wheels within wheels’ are indirect or secret agencies, out of sight, but in control of affairs.
‘Why doesn’t that fellow ever give a straight answer? He’s the proprietor of the business – the one who should make the decisions – so why can’t he say yes or no, there and the? ‘
‘Because he’s only a figure-head. The real boss works behind the scenes. Wheels within wheels, you know.’