When a certain player touches a part that activates this line, it obviously has the player parameter already in the function, but, when a different player touches the part, the action that happens after the client is fired only appears on the previous players screen, and for the other player that touched it, nothing happens
So basically what this sounds like is that a server script fires a remote event to a single client when a part is touched. This remote event that is fired will only be executed on a local script to the player you specified, and whatever that script does, it will only be visible to that one client, and not any other client.
If you want a single touch to affect all clients you'll have to use FireClients(). If you want this to be seen by all clients, just have it be done through the script rather than firing a remote event, or if you wanna be really complicated, have another remote event be fired from the client with info to update to the server, but then that opens you up to exploitability which isn't good, so just stick with the touch event code you want to be executed on the regular server script.