When not in battle mode, a minimap is displayed in the upper right corner. Red dots represent enemies which you will (usually) have to fight in order to be able to proceed. Each enemy or enemy group also has a field of encounter. Once your leader steps into a field of encounter, the minimap will blink red and your leader’s stance will change to a battle-ready stance (for example, Lightning will run with her right hand close to her blade).
Each enemy also has field of vision. If the enemy spots your leader, a red '!' will appear above the enemy’s head (if you’re dealing with a group of enemies, all of them will become alerted to your presence in their field of encounter), and will now come to actively try to fight you.
You can exit their field of encounter and wait until their alertness goes down, at which point they return to whatever they were doing before. It’s funny how you can literally dance in front of an enemy’s nose and it won’t come after you, as long as you stay out of its field of encounter.
If you manage to sneak behind the enemy and touch it without the enemy seeing you, you get the "Preemptive Strike" advantage. This will be explained in more detail later.