Torment
Torment is, basically, the demonic equivalent of Vampire's humanity trait. Rated on a scale of 1 through 10, it measures how close the demon is to their true angelic heritage.
Torment has two aspects -- permanent and temporary. The temporary points tend to fluctuate during the course of the game. If a demon performs selfish acts, or goes against his code of ethics, or otherwise "sins", there is a chance his torment will increase. If he fails the appropriate virtue check (similar to the checks required in other World of Darkness games, like Vampire), he gains a point of temporary Torment. If his temporary Torment reaches 10, he gains a point of permanent Torment. If this score reaches 10 the demon is lost to the pain and madness of the abyss, and is removed from play. (Permanent Torment starts around 3 or 4, depending on the demonic house of the character in question.)
If, on the other hand, the demon performs selfless acts, seeks the greater good, and other "heroic" actions, he can reduce his temporary Torment. He can also spend experience points to reduce his permanent Torment rating -- in theory, if his Torment were to reach 0, he would be redeemed. The rules, however, categorically state this is impossible. How can innocence, once lost, be regained?
Torment does more than measure how far gone your demon is, however. It also affects your use of lores. If you recall, each invocation has a normal and tormented version. When rolling for an invocation, the value of each success on the roll is compared to the PC's permanent Torment. If the values are all higher, the power goes into effect as normal. If any of the values are equal to or lower than the PC's Torment, the tormented version of the power goes into effect automatically, with all the negative side-effects that may entail. You can choose to invoke the tormented version of the ability at will, but doing so automatically gives you a point of temporary Torment.
Your character's permanent Torment score also affects the appearance of your character's visage -- the higher your Torment, the more monstrous your apocalyptic form is.