Replication is the process by which games transmit data over the network to keep clients in sync with the server. For the Unreal Engine, we can see that a lot of the work is already done for us. The player location, movement, and jumping is replicated in the third-person template we've been using. However, anything we add to our project must be replicated properly to prevent bugs like this from occurring.
Not everything needs to be replicated, though. The server doesn't care if you're in your game's settings menu adjusting the resolution or key binds, and the other clients certainly don't need to know. Knowing what to replicate is actually more important than knowing how to replicate, since you run the risk of lag and other network problems if you overshare, so to speak.
There are also ways to fake things to further improve performance. Take...
