Client-side prediction
Client-side prediction is an aspect of many modern first-person shooters.
In Client-side prediction, the game determines if the player has successfully attacked an in-game character by what the character sees. This is slightly simpler than the game determining a successful or unsuccessful independantly.
As technology improves, some gamers are beginning to dislike client-side prediction. A good example of this occured when the Half-Life modification Team Fortress Classic was modified to use client-side prediction. Designed to reduce latency in games, some gamers felt that client-side prediction gave an undue benefit to those on non-broadband connections.
On slower connections, players often see enemies not where they really are, but where they were previously located. With client-side prediction, the game determines if an enemy is hurt by what the slower player sees. Even if a target has since moved far away, he is still punished because the slower player's client-side prediction determined he was hit.