An outlaw is a player who attacked a "red" player who is much stronger than them. The benefit is that you got whatever you wanted from that red player if you were successful. The downside is now anyone, of any size, can now attack you. This lets that red player you just messed with come back for vengeance. Luckily after a week you loose outlaw status so it isn't the end of the world. I've found out that the game forces some inactives to throw their fleets at near targets, which can cause a little field of outlaws to pop up if they are near a bigger player.