Similar to airplane mode, but just for texts.
This feature would be useful when you are sharing your phone with other people (ex. watching a video together / looking at photos together / someone borrowing your phone to use / when driving with a friend and phone is connected to car via Bluetooth).
if you are in a situation where you do not want another person reading your incoming texts, you could just use this option to temporarily restrict notifications of new texts until your phone is private again.