Shaped items have an expanded mod pool and have unique interactions with items like Eternity Shroud or Disintegrator.
The first two influence item were introduced in Version 3.1.0, the War for the Atlas.
With Version 3.9.0, four more influence types were added. Additionally every item now can have up to two different influence types.
Awakener's Orb is able to transfer influence to a different item. The four Conqueror orbs (Warlord's Exalted Orb, Hunter's Exalted Orb, Redeemer's Exalted Orb, Crusader's Exalted Orb) add a new affix to a rare item from their respective influence pool alongside adding said influence to the item base.