You’re not going to encounter your first fortress until you’re many hours into the game (we were at over 20 hours in at that point, but we play slowly), and you won’t encounter your second until many hours after that.
Doing so sends a message to Sauron and can earn you some rewards. They’re, well, fortresses in each area of Mordor that you can (try to) take over and control. Fortresses are one of the new mechanics added to Middle-earth: Shadow of War.
