First of all, you need great controls. You want to make sure that the player will learn the controls quickly and when playing the game, the player forgets that they are holding a controller. Movement and turning cannot feel awkward. Otherwise, figuring out the controls throughout the game can break the immersion. While this may be optional, it would help the movement immersion if the camera "jumps" up and down slightly like in Mirrors Edge if you look closely. In addition, it would be helpful if you can vault over low waist cover. Make sure the camera tilts to the side like in Medal of Honor, Warfighter and Mirors Edge. Call of Duty may allow players to do this but the camera simply floats up and lowers the weapon down off screen. Despite the differences in looks between games, this mechanic can greatly help traversing the environment as well as showing that the character you play as can actually jump like we can in real life.
Another factor is the weapon held in the hand. In the past, the weapon would just simply be lowered to show at the person is moving but nowadays, the weapon would be tilting left or right if strafing and it would "jump" up and down when moving forward. When sprinting, the weapon is not aimed at the reticule, but is lowered instead. This can show the illusion that you are playing this character instead of being a camera.
We also have the melee attack. While this is mostly best done for third person games like assasins creed and DMC, melee can also help the immersion if the animations is done correctly. The knife animation can be a simple swipe but may not help enough if the player can't stab the enemy in the game (I am looking at you MW 1). But it doesn't have to be just knives, if the First Person game has swords or axes, have different animations of various slashes like Dishonored and Dead Island. Do a horizontal and vertical slash animation. Case in point, do what the 3rd person games do; have different animations for melee attacks instead of a simple blade swipe. It's very important if the first person game focuses on melee weapons more than guns.
Recently, a YouTube e channel called smosh games released a video talking about what makes a good FPS game and somewhere, it has more on that melee attack thing I mentioned earlier. Check it out if you need some ideas what makes the genre immersive.
">