This is the second boss in Icecrown Citadel, and consists of 2 phases. Both phases are quite easy on the healing and DPS requirements.
Damage to the boss does not decrease her health but instead depletes her mana as she begins phase 1 with a Mana Barrier. Once her mana is completely depleted, phase 2 begins.
Shortly into phase 1, she will summon 3 adds: 2 Fanatics and 1 Adherent. She will then empower one of them a short while later. The empowered Adherent or Fanatic gains new abilities, some of which can severely jeopardize the completion of the encounter. From a priest's perspective, an empowered adherent is strongly undesired since they become immune to magic damage as well as gaining a spell called Curse of Torpor, which adds an extra 10 second cooldown to all spells. Hence it is crucial to burn down all adherents before she can empower them.
Once the adds are down, she will summon another wave of three adds a short while later. This time it will be 2 Adherents and 1 Fanatic. Again, Adherents must be killed first. If an adherent becomes empowered, the game is as good as over.
Once Deathwhisper's mana is depleted, phase 2 begins. This is simply a tank and spank phase. She does moderate damage (~10% health per melee hit).