The genoa is very important because it provides a relatively large share of the driving force for your boat. There are two reasons for this: First, the genoa has no mast in front of it to create turbulence and spoil clean flow. Second, it sails in a continual lift that is caused by the mainsail's upwash
Upwash is the bend that a sail induces in the approaching air flow. For example, the wind begins to curve around a mainsail well before it actually touches the sail. Sitting in this upwash region, the genoa thinks it is in a lift, so it can be trimmed farther off the centreline of the boat than the main.
This makes the genoa more efficient by rotating its forces (perpendicular to the chord line) more forward and less sideways. If your main is the sailplan's rudder, then the genoa is its motor. Of course, their functions overlap, but in general you should trim your genoa for drive and your main primarily for helm balance.