As far as I know it doesn't have anything to do with accuracy. The pictures you see are like slices of the object you're aming for, all at different height levels. So bottom left is the ground, then you see the legs of the soldier, going up the body to the torso with two arms (I guess) up to the head and then nothing (above the head).
This can be quite useful if your target is partly covered by another object. If you shoot normally, your soldier automatically aims for the centre of your target. If, however, your target is partly covered, then the shot won't make it through. If, on the other hand, you use the special aiming thingy and go for the head instead, your shot might not be blocked.
I don't think it influences the damage you inflict in any way. Not even sure if it is more difficult to hit the head than the torso either.
Feel free to correct me anyone if I'm wrong here