While you can generate lift with a symmetric airfoil by picking an appropriate angle-of-attack, efficient designs tend to be more like an airplane wing - strongly curved on the liftward (downwind and forward) side, nearly flat on the anti-liftward (upwind) side.  If I understand it correctly:  This builds in a tendency to bend the passing airflow in the appropriate direction and keep it "attached" to the surface for a broader range of angles-of-attack.