The run option is used during battle to escape without fighting. The button resembles a figure dashing out of sight, and when selected, gives you a percent chance of either escaping the battle, or doing nothing at all. The chance of escape increases if you are fighting an enemy that is weaker than you, i.e. if your party is comprised of level 20 characters and is fighting against Vermin or Wild Wolves, you will get near a 100% chance of escape, whereas if you were fighting against monsters such as Fenrirs or Cruel Dragons, your escape percentage would be much lower.
If your attempt to run is unsuccessful, your entire party will do nothing, not even defend, allowing the enemy to attack that turn. In addition, if you try to run during a boss battle, a message will appear saying, "This is no time to be running away!" and return you to the action select menu.
For the running action in the overworld, see Run.