"What? He's crazy, this guy must be crazy to suggest that hipfire with a mysterious reticule in the middle of the screen is in any way realistic."
Well, not so crazy when you think about how the screen perspective is a single 2D perspective yet humans have 2 eyes meaning you'd get two shifted 2D perspectives, that means the parallax must be represented combining the two views into one frame.
"What? I don't follow, Parallax?"
Basically, both your eyes look the same direction but because your eyes are a few inches apart they get a different view. Like how if you look at a tree with your finger held up, your right eye sees what is slightly shifted from what your left eye sees:
Remember this picture. How does it look familiar? The finger in line to the tree, like the sight post on a gun, and then the off the the side view...
When we see the the world around us with two eyes we combine this together what each eyeball sees as the images are processed separately. But how would you Represent this in a First-person perspective which has only a single 2D frame?
Think about it, the right eye would be looking down the weapons sights and out around at the enviroment. The left eye would be looking around with a better view at the environment and see the left side of the gun in your hand.
Your left eye would see something like this:
While your right eye looking down the sights sees this:
Now take the important part of what the right eye sees, where the sights line up and indicate where the bullets go, and lay that superimposed over the wider less restricted view of the Left eye. Then you have the classic "unrealistic" representation of aiming a weapon with a reticule in the centre of the screen:
"These games are so unrealistic, you can't aim without using the sights. Where does the reticule on the screen come from?"
The reticule comes from using the gun. It is a game REPRESENTATION of your right eye using the sights while your left eye is open.
You can do this yourself with a ruler though preferably something more gun-like, With your right eye look down the ruler/sights then close your right eye and open your left. It's more obvious with your head canted to the right so your left view of the gun is a little lower.
"Then why bother with Aim-down sights in games?"
Why? I think it's a con, with faux-realism and a crutch for much more unrealistic things like instantaneous zoom with iron sights and super-powerful aim-assist when activating iron-sights.
It's most valuable for on consoles where the thumbstick is just so crap for aiming, not a problem if a proper aiming device like a mouse is used.
OK, some hyper realistic games might need aim-down sights like Red Orchestra or ARMA for how you have adjustible sights and other things, but certainly the vast majority of FPS games, including war games the ADS mechanic is a crutch for gameplay, not for the level of realism they are aspiring to.