Refer to figure.
The vertical stabilizer (fin) provides stability in the yaw axis, which is the vertical axis around which the aircraft turns left or right (yawing motion). Without the vertical stabilizer, the aircraft would be prone to unwanted yawing, which can cause instability and make it difficult for the pilot to maintain a straight and controlled flight path. By counteracting aerodynamically induced yaw motions and helping the aircraft to maintain its intended heading, the vertical stabilizer ensures smoother and more stable flight.

Therefore, the correct response is Improvement of directional stability because the vertical stabilizer's main function is to stabilize the aircraft's direction, preventing it from unwanted side-to-side movement and assisting in maintaining a controlled and predictable flight trajectory.