The server contains the actual running model of the game (the only source of truth).
Each player sends commands to be executed in the server's model, and when they see those actions take place, it's a result of the server accepting that command and echoing back the effect of it.
This echo is also broadcast to all other players in tandem.
If Player A is laggy (experiencing high latency), their actions take longer to reach the server, and their view of the game will be slightly behind the actual game.
If Player B is not laggy (fast connection, low latency), they may very well see the effects of Player A's actions before Player A can!
Now if we had no server, one of the player's must be the source of truth (or worse still a shared truth). This is where being laggy AND the server causes everyone else to be laggy regardless of how awesome their connection is. Being a laggy server is like being a bottleneck.