Restedness is your character's ability to learn from combat, and our way on this server of giving characters who like to spend time roleplaying an extra bonus when they do actually decide to plumb the depths of a dungeon. When your character is very rested, monster kills will grant more XP. When your character is not rested, monster kills will only grant the normal amount of XP. Restedness goes down while you are fighting and recharges when you are not fighting.
Restedness also has a cumulative effect, the bonus increasing exponentially the more rested your character is. A character who has, for example, 1000/4000 restedness gains only a +50% XP bonus, a character with 2000/4000 restedness gains a +100% XP bonus, and a character with 3000/4000 restedness gains a +200% XP bonus.