The Cursed Shrines is a special event in Adventure Mode of Diablo III. It can only appear if nominated a bounty, in any zone of any Act. If it appears, one can go through a red portal and access one of the secret zones: Leoric's Gardens, Blighted Sewer, The Killing Grounds, The Archives, The Bound Keep, or Nephalem Proving Ground.
The event itself requires cleansing a Cursed Chest. Once the area is entered, a timer will start, and 6 Cursed Shrines will appear throughout the arena. Each will be cleansed and disappear (without granting any Shrine effects) when touched, but will also spawn a large pack of monsters of random type, and cast one random monster affix. All six must be touched before time is up, then remaining monsters cleared, to receive a bonus Radiant Chest.
Interestingly, each Shrine will benefit from Nemesis Bracers, if the character has them, and will summon a Rare pack.