When you reach level forty you will be able to enter heroic versions of the dungeons. These versions contain even more powerful monsters than the regular versions of the dungeons, but they contain even greater rewards. Each heroic dungeon can only be completed once per day.
You will only have access to one heroic dungeon at first. You will need to obtain reputation with the Adventurers' faction before other heroic dungeons will be unlocked. You can gain this reputation by completing heroic dungeons that you already have access to.