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Technically, Quest Item is one of several values for item's binding property, other being Binds when picked up, Binds when equipped, Binds when used and Binds to account. They act like soulbound items and cannot be sold, traded or put on Auction House. However, there are significant number of items used for quests but not marked as Quest Item.
Some quest items are considered party loot. If a quest asks you to retrieve something by killing a specific target, and looting his head for example, that head will be able to be picked up by the entire group; making that item party loot. This also applies for quest items where the loot is set to Free for All, and only one of the users currently has the quest, so if the player without the quest would loot the NPC first, the other player would still be able to retrieve the quest item.
If players delete any quest item from their bags before turning in the associated quest, the quest will automatically be abandoned. This occurs even if the item deleted is in excess of that needed to complete the quest.