Makes you feel more cool when you play for the first time
This help the player hit the enemy in a first and third-person shooters. If the reticle is close enough to the target the game will nudge it onto the target. It is a common mechanic on consoles games where the controller input is less precise then a mouse.
Modify the control input when aiming towards a target to make it easy to keep aiming on the target.
Magnetism: Modify the camera turn speed so it matches the target.
Centering: Modify the camera turn speed so that player turns toward center of the target.
Friction: Reduce the players turn speed when player has a target in sight.
Aim Down Sight (ADS) Snapping
When looking down the sight of the weapon and the reticle is close to the target it will change the aim of the player and place the reticle on the target.
Magic Bullet / bullet magnetism
Bends the bullet towards a target.
BF4 Aim Assist Explained - 2014
Techniques for Building Aim Assist in Console Shooters - 2013
The Effectiveness (or Lack Thereof) of Aim - Assist Techniques in First - Person Shooter Games