Emblem Gear (WoW)  

The idea behind Emblem Gear, or Badge Gear as it used to be called during The Burning Crusade was to combat the perceived unfairness of random loot drop.

By making each boss drop a token and than letting player spend token to buy gear they wanted from certain npc, players would be ensured that they would eventually get something out of raiding or running 5-man instances. The idea was introduced with Badges of Justice in TBC, was extremely well received with the player base and has now become an integral part of the game.

Badge of Justice & The Burning Crusade

Badge of Justice would drop from boss fight in level 70 Heroic Instance has well as the raid boss in Karazhan. At the time, farming instance for Badges was seen as the best way to get ready for the raid scenes. At a later date, Blizzard released a new batch of Badge Gear which was way superior to what one could get from Instance or Karazhan, allowing people to get ready for much harder content much faster.

While Badges of Justice and their vendor are still available in the game to this day, those are now legacy content/item.

Emblem of Heroism

Emblems of Heroism are the first tier of token dropped in Wrath of the Lich King - they can be gotten from bosses in the level 80 Heroic instance or from any boss in the the normal version of Naxxramas, Vault of Archivon, Eye of the Eternty or the Obsidian Sanctum.

The Gear from the Emblem of Heroism is fairly good, equal in item level to the epic that drop from the last boss of an Heroic and slightly lower than 10man Raiding Gear. Farming the emblem for those gear allow one to get ready for raid content much faster, or to get an upgrade from some of those harder to get gear slot.

Emblem of Heroism can also be used to buy Frozen Orbs, which make obtaining them and getting those crafted epics much easier.

Every shop in Dalaran has a Vendor who sells a handful of Emblem item, but usually the handiest way to get your gear is simply to go directly to your faction's Emblem Vendor. They can be found in Dalaran, Arcanist Ivrenne, serves the Alliance while Magistrix Lambriesse serves the Horde.