Blackhand's Breadth is a trinket which increases the wearer's critical hit chance.
This item is a quest reward from the Alliance quest General Drakkisath's Demise which starts with Marshal Maxwell at Morgan's Vigil in Burning Steppes. To complete the quest, you must kill General Drakkisath in Blackrock Spire and return to Marshal Maxwell.
It is also a quest reward from the Horde quest For The Horde! which starts with Thrall in Orgrimmar in Durotar. To complete the quest, you must turn in the following item to Thrall:
The quest chain for the Horde begins in Kargath.
The quest chain begins by looting [General Drakkisath's Command] from Overlord Wyrmthalak in Lower Blackrock Spire.