Severing is when a person loses the ability to touch the Source. In the Age of Legends, this was the only word, used for male and female, for deliberate and accidental (TWoRJTWoT, Ch. 2, LoC, Prologue). In the current age, there are three terms, stilling for when it is done deliberately to women, gentling when done deliberately to men and burning out for either sex when done accidentally (TSR, Ch. 5; TPoD, Ch. 14).
A woman, or man who is severed generally loses the will to live and will typically die over two to three years after (TSR, Ch. 17; TGH, Ch. 38; TFoH, Ch. 26)). Bonwhin, for example, survived four years after being stilled (TWoRJTWoT, Ch. 12). Logain managed for a while, but as time went by he became more and more despondent, eventually, doing little more than eat and walk (TFoH, Ch. 26). Aes Sedai themselves, or even women who spend time around them often shudder when they think on it, or even have trouble even saying the word (TGH, Ch. 4; TSR, Ch. 5; TSR, Ch. 47). Samitsu and Niande throw up when they learn Rand stilled three Aes Sedai (ACoS, Ch. 36).
Although most die relatively quickly, some last longer, for instance Cadsuane claims that the men she has taken have tended to live longer, and Emarin Pendaloan lived for ten years after being gentled. Setalle Anan came very close to death, but recovered and made a life for herself (KoD, Ch. 9). Little is known about women who have been severed, as Aes Sedai avoid them (TGH, Ch. 4) but some Yellow sisters, the best Healers, would try to learn to Heal anything. Until Nynaeve Healed Logain however, even a hint of success at Healing a woman who had been stilled was non-existent (TSR, Ch. 5). Verin thinks that Irgain is treated well by the Aiel, but probably wishes she was dead (TPoD, Prologue).
It is said that to survive severing, a person needs to find something they want as much as they wanted to channel. For Siuan, that was pulling Elaida down, for Logain, it was revenge against the Reds, before he became involved in the scheme he was dying, but once he started to talk to nobles and tell them that the Reds set him up, he begins to reclaim the desire to live (LoC, Ch. 29). We cannot know if this would have been enough for them once the plans were over, but we do know, that for Setalle at least, finding a man to love and a family was enough (KoD, Ch. 9).
Despite having different terms, Aes Sedai tend to see it as the same, “It was like having two words for falling down stairs depending on whether you tripped or were pushed. For that, most Aes Sedai seemed to see it the same, except when teaching novices or Accepted” (Egwene (TSR, Ch. 5) and when stilling is healed, they assume the Healing would work on women who are burned out “Every sister carried the fear somewhere deep inside that she might be cut off from the Power. And now a way to Heal what could not be Healed had been discovered. By a man!” (Cadsuane, WH, Ch. 13). Although this may be the case, there are significant differences between stilling and burning out that indicate they may be wrong.
Stilling is the process by which an Aes Sedai (or other woman) is permanently prevented from touching the source. A stilled woman cans sense the source, but not touch it, (TWoRJTWoT, Ch. 2), and Siuan and Leane can sense what Moghedien feels through the a'dam. They can't make her feel or do anything though (LoC, Prologue). The weave for stilling is much like that for shielding, but sharper TDR, Ch. 55; TSR, Ch. 54). Rand stills the three Aes Sedai that are shielding him, he crushes the three soft points in fists of spirit. He escapes and sees one of them, an angular woman with her head in her hands screaming (LoC, Ch. 55). Stilling is very rare and only done for severe crimes, relatively few Aes Sedai have ever been burned out, and far fewer stilled (TSR, Ch. 5), none for one hundred and forty years (LoC, Ch. 7). Every novice had to learn the name of each Aes Sedai since the breaking who had been stilled, and her crime (TGH, Ch. 4). In the history of the Tower, two Amyrlin Seat are recorded as having been stilled, Tetsuan and Bonwhin were kept in the White Tower as servants as no one can rally round a woman who must scrub pots (TGH, Ch. 4) and during the formation of the Tower, stilling was used on some of those who did not want to unify, to bring the others into line (TWoRJTWoT, Ch. 9). Siuan worries that she would be stilled for planning to shepherd the Dragon Reborn (TGH, Ch. 4) and Elayne thinks that an Accepted bonding a Warder was not quite a stilling offence (TFoH, Ch. 35). No one seems to suggest that Alanna bonding Rand, however, was even close to being a stilling offence. Moiraine claims that just knowing balefire might be enough to get her stilled (TDR, Ch. 39).
Aes Sedai who have been stilled, lose the Ageless look and are no longer bound by the Three Oaths, even if they are then restored (KoD, Prologue). Sashalle looks somewhere short of her middle years, with perhaps scraps remaining to make her look more beautiful than she really was, reminding Samitsu of a rumour that said that a woman who was stilled grew young again and loses the Ageless look (CoT, Prologue). When Min sees Siuan and Leane for the first time after they have been Stilled, she is not sure it is them “The faces looked right – almost right – and untouched by whatever had been done to them. But the Agelessness that marked Aes Sedai seemed to have melted away; she would have had no hesitation at all in thinking these women were just six or seven years older than herself at most” (Min (TSR, Ch. 47). Siuan is surprised by how quickly the look faded and thinks the rough treatment she and Leane received could have sped it up (TSR, Ch. 47). After Stilling, Amico looked young, perhaps younger than her years, but it was not quite the agelessness of Aes Sedai who had worked years with the One Power (TSR, Ch. 5).
As with stilling, a gentled man can sense saidin, but not touch it. For three hundred years after the White Tower was built, the Aes Sedai tried to find alternatives to gentling but gave up because there weren't any (TGH, Ch. 24).
Most gentled men commit suicide if they can. Those who don't lose the will to live and die in a couple of years (TWoRJTWoT, Ch. 2). When Elayne sees Logain sitting on a bench in the Inner Courtyard of the White Tower, he is crying, and runs away when he sees her (TGH, Ch. 38). Later, he deteriorates and on the way to Salidar, he is losing interest in life, seeming to have just a few days left (TFoH, Ch. 26). After he has been Healed and can channel again, the other Aes Sedai agree he can't really be gentled (LoC, Ch. 30), though some such as Delana (LoC, Ch. 37) and Romanda (LoC, Ch. 54) push for it .
One of the main functions of the Red Ajah is to seek out men who can channel and gentle them. According to Tower law, they must take the man back to the Tower before doing this (TSR, Ch. 17). However, this does not always happen. In the previous ten years, six men were found, and the previous twenty years, twenty four were found, but the official chronicles record only sixteen (ACoS, Prologue). What happened with the other eight is unclear, but it is likely, that as with Owyn, they were just gentled and abandoned.
Gentlings are carried out in the Traitor's Court and require an order from the Amyrlin Seat (TDR, Ch. 22). They are conducted by a circle of 13 women: 12 Aes Sedai and the Amyrlin Seat. During the ceremony, the Amyrlin Seat recites the following words:
This man, abandoned of the Light, has touched saidin, the male half of the True Source. Thus do we hold him. Most abominably has this man channeled the One Power, knowing that saidin is tainted by the Dark One, tainted for men's pride, tainted for men's sin. Thus do we chain him.
There is more that the Amyrlin recites, but the books do not quote it.
Warders ring the courtyard of the Traitor's Court during a gentling to prevent attempts to free the man being gentled. They do this because Guaire Amalasan's and Raolin Darksbane's followers tried to free them when they were gentled.
Custom dictates that every member of the Tower, even servants, must be present in the Traitor's Court during a gentling "to watch the will of Tar Valon made fact." It may be assumed that their presence would also be required for a stilling or execution.
Burning out is the term used when a person holds more of the One Power than they can safely handle. Unlike stilling, a burned out woman can not even sense the source (TWoRJTWoT, Ch. 2). A woman wearing an a'dam cannot move if the leash is held by a burned out woman, though we do not know if the burned out woman can sense anything (WH, Ch. 29). Burning out is very rare (TSR, Ch. 5), but is still a fear that all Aes Sedai live with at the back of their minds (WH, Ch. 13). It is much more common with the Asha'man as they push their trainees much faster (TPoD, Ch. 14). This quick learning, forcing is very dangerous and the one thing Siuan seemed genuinely sorry for was doing it to Egwene (ACoS, Ch. 9).
The most recent woman to be burned out it Martine Janata, who was burned out studying ter'angreal, twenty-five years earlier. She was unconscious for three days and could not remember the entire week (TPoD, Ch. 2). Setalle Anan was an Aes Sedai once and is interested in ter'angreal. She says that the other Aes Sedai would realise if they let themselves, but they don't like to think of such things. Women are expected to go away decently and die soon after, but Jasfer found her in time (KoD, Ch. 9).
After his capture, Guaire Amalasan was taken back to the White Tower and sentenced to gentling (TWoRJTWoT, Ch. 11).