If you touch an enemy you get into a fight. If you touch an enemy, no matter what direction you or they are facing, while running, then you break formation (essentially a back attack). So basically you need to walk everywhere to prevent that.
(Assuming that's what Aeana is referring to)
She could also be referring to the hidden battle counter which increases the strength of enemies (and bosses) at certain intervals, and the fact that running still counts as a battle, so any time you run from a fight you are actively making the game harder on yourself. Learn to save scum A LOT in this game.