What does it mean when a mob is marked with a crown?
According to this Swords of Ditto FAQ, it gives you more money and items:
This crown is a special game mechanic that can be exploited to help you earn more money and consumable items. When you hit an enemy with a crown next to his life bar, he will drop a random item for every attack that connects. This item can be something as simple as money, or something more valuable such as bombs, food, or even unopened sticker packs!
After you defeat the enemy with the crown, a yellow orb will shoot off to another enemy. This is the crown moving to a new enemy. This new enemy will now have the crown and can be attacked for extra rewards just like the first. To maximize your rewards, always attack the enemy with the crown, and then follow the yellow orb to the next enemy, who will then have the crown, and attack that enemy next. By killing enemies in this order you will greatly increase the amount of treasure dropped.