Why is Leakage Current Important when a MOSFET switch is "ON?"
The datasheet asks you to refer to figure 34. 



Appears as though they mean the maximum current for the differential across the open switches +/-10V. 

This is important because the current across the open switches or to the power supplies can represent an error in a precision analog signal. The typical current is fairly high even at room temperature (20pA typical and 600pA over the industrial temperature range). If your signal is 100uA then 600pA represents a 6ppm error.