I think the susceptance is related to the amount of energy the box can store. If conductance (or resistance) is a measure of how much power is dissipated in the box, susceptance (or reactance) is a measure of how much reactive energy (e.g., capacitor or inductor) the box can store. For a given source voltage, a box with a larger susceptance would store more reactive energy than one with a smaller susceptance.
Of course, it is also used to relate the complex currents and voltages through
I = YV where Y = G + jB (B is the susceptance).
John