Quest items are items that have the main purpose of being used for completing a quest.
Fallout 3 and New Vegas
"Quest item" is also a specific property (or "flag" in programming terms) of an item. An item with this flag cannot be dropped, sold or stored in containers. Weapons and armor that bear a quest item flag are also not repairable by merchants, but are repairable through the Pip-Boy. Contrary to ingame information these items do not actually weigh anything. Not all quest items in the general sense of the term have this flag (e.g. the Geomapper module).
The purpose of this setting is to prevent the player character from rendering quests incompletable by selling or dropping items which are required for its completion.
The SetQuestObject <base id> 0 console command can be used to clear the quest flag from items. This is useful when your inventory is cluttered with items from quests that have been completed and no longer have a purpose.