The offset hinge allows the leading edge of the aileron to stick above or below the wing as they are deflected.  

This protrusion of the leading edge into the airflow reduces the control pressure required to fly the airplane.  Some pilots tell me that it also increases roll rate due to a better airflow making the aileron more efficient.   This was originally supposed to eliminate the requirement for spades which also are designed to reduce control stick pressure but I still see aircraft using both systems together. 

You can see one of the actual hinges, which wasn't installed yet, sitting in the shadows on the table below the ribs.