One's cheek weld force on the butt stock determines how much pressure there is on the stock. That effects how much the bore axis moves off its direction to the target when the primer fired and the bullet's going down the barrel. Different cheek weld pressures means the rifle's movement during the bullet's barrel time will be different. While the inheirent accuracy of the rifle and ammo are still intact, it centers at different places on the target with different amounts of pressure on the stock from us humans.
So does putting the butt pad at different places in ones shoulder from shot to shot. As does different sling tension.
Bart hit the nail on the head. I would like to add that your cheek wield is very critical when shooting through iron sights, since it changes perspective. However with modern optics, as long as they are used correctly, they should be parallax free. Cheek wield is now more about maintaining consistent recoil. So it is not as important as it used to be, but it can still affect accuracy.