How does aim assist actually work?
Through several distinct mechanisms layered together, most of which are invisible — and the fact that players cannot feel them working is precisely why the subject is so contentious.
The main techniques:
Rotational aim assist, the strongest and least visible. When an enemy is near your crosshair, the game rotates your aim to help track them as they move. On a controller it feels like your own thumb movement, which is why players frequently do not know it is happening.
Slowdown, or friction, reducing look sensitivity as the reticle passes over a target, making it easier to stop on them.
Magnetism, gently pulling the reticle towards a target.
Bullet magnetism, adjusting the projectile's path after firing so a near miss connects — operating on the shot rather than on your aim.
Target snapping, jumping to the nearest target on aiming down sights. The most obvious and most sparingly used.
Hitbox generosity, where the registration volume is larger than the visible model.
Why it exists. A mouse maps hand position directly to aim, with effectively unlimited precision and instant large movements. A thumbstick maps deflection to rotation speed, which is a fundamentally worse control scheme for aiming: fine adjustments and fast turns trade off against each other. Without assistance, controller players cannot compete.
Why it is contested. In crossplay lobbies, strong rotational assist can exceed what a human can do manually in close-range tracking, so a controller can be advantaged at short range while a mouse dominates at long. Both groups are convinced the other is favoured, and both are partly right, because the advantage is range-dependent.
What developers do about it: separate input-based matchmaking; disclosing or tuning assist strength; reducing it at close range; and allowing players to opt out of crossplay.
Worth knowing: assist strength varies by game and weapon; it typically does not apply to enemies you have not seen; and input-based matchmaking, not removing assist, is the fix most competitive communities actually want.