Hit detection in multiplayer deals with the compensation of lag for doing tracing to see if you actually hit the player on your screen or not. Hit detection is actually just ray tracing, however, people use it synonymously with the assumption that they are talking about hit detection & netcode at the same time.
The server never actually knows where the player currently is, the amount of difference between what the server knows and where the player actually is on his screen is about the amount of your ping.
Basically, if two players have a 50 ms ping, both player A and player B will be 100ms behind in terms of relative positioning due to the fact that it takes player A 50ms to send his position to the server and then another 50ms to send player A's position to player B. There is a good amount of prediction that goes into calculating where the player is actually rendered and what the server considers "valid hits". Better netcode will make these effects less noticeable.
In FPS's online, sometimes it looks like you made it safely behind a wall only to die and warp slightly behind where you thought you were, this is due to that compensation or pseudo-hit detection (you were not behind the wall yet for the player that killed you).