Allowing LAN traffic lets you connect to other devices on the same network. This is handy for printing, network file access and the main reason we added it in the first place, Chromecast.
How to enable Allow Lan Traffic Shown on Desktop app - same instructions apply to the Android app. This option is not available on the iOS app
And that's it! You have enabled Allow Lan traffic. You should now be able to communicate with all other devices on your network.