The Royal Seal of Eldre'Thalas is a class specific trinket which has a +10 bonus to fire resistance, as well as another bonus, which varies by class.

Acquiring a Royal Seal of Eldre'Thalas

In the Dire Maul instance in Feralas all bosses have a chance to drop one of the following books.

The books need to be returned to either Lorekeeper Mykos (Hunter, Warlock, Paladin), Lorekeeper Javon (Druid, Priest, Shaman), or Lorekeeper Kildrath (Rogue, Warrior, Mage) in the Athenaeum (Also referred to as the Library) in Dire Maul. The easiest way to get here is by taking the north entrance to Dire Maul, heading down the ramp into the open area then taking the double doors to your left, which lead to the library.

Class bonus

Aside from 10 Fire Resistance, each trinket gives a bonus based on the class the trinket is for.

Class Trinket Effect
Druid Druid [Royal Seal of Eldre'Thalas] * Increases spell power by 23.
Hunter Hunter [Royal Seal of Eldre'Thalas] * Increases ranged Attack Power by 48.
Mage Mage [Royal Seal of Eldre'Thalas] * Restores 8 mana per 5 sec.
Paladin Paladin [Royal Seal of Eldre'Thalas] * +150 Armor
* Increases spell power by 12.
Priest Priest [Royal Seal of Eldre'Thalas] * Increases spell power by 18.
* Restores 4 mana per 5 sec.
Rogue Rogue [Royal Seal of Eldre'Thalas] * Increases your hit rating by 20.
Shaman Shaman [Royal Seal of Eldre'Thalas] * Increases spell power by 23.
Warlock Warlock [Royal Seal of Eldre'Thalas] * Increases spell power by 23.
Warrior Warrior [Royal Seal of Eldre'Thalas] * +200 Armor.

Extra information

As of patch 1.10 the quests are no longer repeatable.

There is no Death Knight Seal because they were not out when this was released. This is not likely to change.