Dual functions result from systems that are related in a certain way. For example if you have a resistor, inductor and voltage source in series, the equation for the voltage is
vin - R*i - L*di/dt=0.
If you have a current source a conductance (G=1/r) and a capacitance in parallel the equation for the sum of currents is
iin - G*v - C*dv/dt=0.
The equations have the same form and are dual.
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Generally if you take a description of a circuit, and make the following word replacements (as was done above):
current=voltage
resistance=conductance
capacitor=inductor
parallel=serial
then you end up with dual circuits described by equations of the same form.