In the psychic tug-of-war in the mind of a wraith between the Psyche and Shadow, sometimes the Shadow can gain the upper hand and take bodily control of a wraith for an entire scene. This is called Catharsis.
During this scene, the Psyche can only watch as events unfold, unless the Shadow wants to hide the events of the Catharsis from him.
Shadows during this time can freely pursue their goals, though this almost never involves complete destruction of the wraith. If the Shadow gets the wraith in line for the Soul Forges, it's more likely meant to scare the crap out of the wraith than to see the wraith destroyed. The Shadow is much more likely to take this opportunity to "teach the Psyche a lesson" or sabotage the Psyche's plans or other such unpleasantness, depending on the Shadow's Archetype.
In order to instigate Catharsis, a Shadow must have more Temporary Angst than the wraith has Permanent Willpower. The Shadowguide then spends a point of Angst and calls for a Catharsis roll, pitting his temporary Angst versus the wraith's permanent Willpower. The wraith may spend Eidolon dice if desired.
If successful, the Shadow becomes the dominant personality for the next entire scene.
The Shadow may choose to hide the events of the scene from the Psyche. If he does, the Psyche can resist if he still has Eidolon dice. (Unlikely, as they were likely already spent trying to resist the Catharsis roll in the first place.)
It is worth noting that the Player remains in control of the Wraith, and not the Shadowguide.
During this time, the Shadow has access to the Wraith's Arcanoi, and any Arts that would ordinarily give additional Angst instead reduce it. The Shadow cannot give himself Shadow Dice, nor can the Psyche offer "Psyche Dice" either. He can use Thorns, and even use the Wraith's Pathos (but cannot reduce Pathos to 0) but cannot expend Willpower.