On a technical level, Scream has a chance to skip an enemy's turn (thereby preventing you from being punished on a successful scream) and permanently lowers the monster's luck by 1 point, which makes it harder for them to hit you. Almost all enemies start with 0 luck. When an enemy screams at you the same thing occurs, except your luck resets after battle to be -3 + the number of charms you have.
A little secret for ya: you get a little bonus to your screams when you are below half health!