Horrific Core

Horrific Cores are used to upgrade the rank of Ashjra'kamas, Shroud of Resolve.

Source
A core is awarded for each quest in the Ashjra'kamas upgrade quest chain, requiring victory in Horrific Visions:

Trivia

 * During the PTR, it was referred to as Blacktalon Shroud and has the following flavor text: "Further tests, and immunizes, your cloak against the Vision."