Applying protection to a message prevents it from being automatically deleted whenever you place a new one down once you've hit the maximum number of messages for your character.
After some tests, it seems that the maximum number of messages a player can place is 10. Once you've reached 10 messages placed, attempting to place another down will delete one of your previously placed messages in order to not exceed the maximum amount. Marking one of your messages as protected ensures that it won't be automatically deleted by this process.
You can only mark 9 of your messages as protected. One of your messages has to be eligible for deletion should you try to place another message down.