Hitscan latency compensation is a topic that causes a great deal of confusion as to how it works and what side effects are to be expected. The community has long ago adopted the term "unlagged", which in itself is a source of confusion but hopefully this post can clarify several points. For further detail on the topic, please read this
excellent overview by Valve, from which Odamex's algorithm was derived.
For the examples in this explanation, we will consider two players: Player A with a 150ms ping and Player B with a 20ms ping.
Background info:
Odamex has a fixed frame-rate of 35fps, which means each frame lasts roughly 29ms. That also conveniently corresponds to the network update rate and the game physics update rate.
Odamex also uses a term "world index" to refer to the particular set of actor positions that the client has received from the server and uses to draw the sprites for actors in the game (enemy players, etc).
How it works:
When Player A aims directly at Player B and presses the fire button, his Odamex client will send all of his input (eg, fire-button, mouse angle, etc) to the server as well as the current world index. The server will receive this input from Player A 75ms later. During this time, Player B may have moved significantly and without latency compensation, Player A would miss his shot.
With latency compensation, the server will temporarily move all players except the shooter to their position in the world index that was received from the shooter. In the case of Player A shooting, it means that Player B would be moved to his position 150ms ago. The server then performs hitscan collision detection and then moves all of the players back to their current real position. This compensation allows Player A to aim directly at Player B and successfully hit him, even with adverse network conditions.
One side effect of this compensation can be seen from the point-of-view of Player B. It is possible for Player B to have gotten behind cover of a wall and still be shot by Player A. This is due to the fact that Player A has high latency and thus his input takes a noticeable amount of time to reach the server and during this time, Player B can move behind a wall. The latency compensation will temporarily move Player B to his position at the time Player A pressed fire, which was directly in the line-of-sight of Player A.
Hopefully this description is not too technical and also did not omit any details that are necessary for understanding the way latency compensation works in modern FPS games. Let me know and I can further clarify any points which are not clear.