Refer to figure.
Whilst we usually think of the rudder (mounted to the rear of the tail fin) as creating turning moments in order to yaw the aircraft, that is simply for pilot control. The tail fin is not just a mounting point for the rudder, but is essential in its own right for keeping the aircraft directionally stable (stable in yaw), and is constantly producing small yawing moments on the aircraft to counteract for sideslip and to try and stabilise on the aircraft.

As the magnitude of a moment (turning force) is the force itself multiplied by the distance from the force line to the pivot point, and an aircraft in flight rotates around its centre of gravity, the moment produced by the tail fin is affected by the location of the centre of gravity (CG). The same applies for the rudder, when operated by the pilot.

If the CG is far forwards, then the distance from the CG to the tail fin is larger, so even for the same force, the moment is greater. Conversely, with an aft CG, the moment is less.