Kreia's early life is only mentioned in passing throughout KOTOR 2, but it was revealed that she was once a Jedi Historian. She even became a Jedi Master eventually, and began training Padawans, the most famous of them being Revan, the Dark Lord of the Sith who features prominently in the original KOTOR. She was an unorthodox instructor, and the Jedi eventually cast her from the order when Revan and many of her other pupils fell to the Dark Side during the Mandalorian Wars.
Fall to the Dark Side
Kreia, now stripped of her Jedi status, sought out Revan, and followed him wherever the legends told of his presense. This lead her to Malachor V, Revan's last known stronghold, and also the scene of the final battle of the Mandalorian Wars. There she found many teachings from the once lost true Sith, and believed that Revan had gone in search of them. She severed all ties with the Light Side of the Force, and took up the title of Darth Traya, Lord of Betrayal.
Dark Lord of the Sith, and Betrayal Again
Traya turned Revan's old stronghold into Trayus Academy in order to train new Sith. She took up two particularly powerful Sith, Darth Nihilus and Darth Sion. Traya's ultimate goal of recreating the original Sith set her apart from Nihilus and Sion, who only desired destruction and the death of the Jedi. They turned on her, and cast her out of the order she herself had started, crippling her both physically and mentally. Nihilus took up the mantle of Dark Lord of the Sith, and his new order scoured the galaxy for Jedi, destroying them at all costs.
The broken Kreia abandoned her Sith name, and brooded for some time on the cruelties of the Force. She came to think of it as a corrupted god, pushing the galaxy into constant conflict in an attempt at balance. She formed a great loathing of both the Jedi and Sith, and all the extremes that they represented. She ultimately began devising a plan to bring about the end of the Force forever.
That was when she learned of the supposed last remaining Jedi, one who had been exiled from the order after the Mandalorian Wars ended. She had learned to live without the Force, even though she had depended on it so heavily before.
This is where the events of KOTOR 2 begin, where Kreia has orchestrated a meeting with the Exile after she (Exile) was nearly captured by an HK Assassin droid, and she saved her from an attack by Darth Sion and a group of Sith.
She adopts her as a student, teaching her about the inherent danger in both the Light Side and the Dark Side. She teaches her to use others as tools, to achieve her own purposes, and in fact, that is exactly what she is doing to her. The Exile has an uncanny ability to form Force Bonds with others, connecting their fate to hers, and inspiring an undying loyalty within them. Kreia wishes to use this talent of hers to create what she calls an "echo", essentially a wound in the Force itself that can radiate across the galaxy. If she can channel the Exile's ability to create an echo large enough, then it could destroy the Force completely.
She led the Exile across the galaxy in search of Jedi that were in hiding because of Nihilus' rampage. She led her to believe that they were the ones who stripped her of the Force when they cast her out, forcing her to learn to live without it, when in truth, it was due to a wound caused to the Force when the Exile nearly destroyed Malachor V to ensure victory at the end of the Mandalorian Wars.
In KOTOR 2, you had the choice of gathering the hidden Jedi together to combat the Sith threat, or to kill them one by one for what you believed they had done to you.
Light Side Path
When the Exile had gathered all the missing Jedi, they revealed the truth about her loss of the force, and Kreia stepped forth, drained them of life, resumed her position as Darth Traya, and went back to Malachor V. She intended to sacrifice herself, now bonded to the Exile, and cause an echo through her that would radiate through the galaxy and end the Force forever. After fighting through both Darth Nihilus and Darth Sion, vanquishing them both, the Exile reached Kreia at the core of Trayus Academy. The Exile defeats Kreia, who then realizes she only ever sought redemption.
Dark Side Path
After destroying the last Jedi, Kreia assumed her position as Darth Traya again, and went back to Malachor V. She intended to sacrifice herself, now bonded to the Exile, and cause an echo through her that would radiate through the galaxy and end the Force forever. After fighting through both Darth Nihilus and Darth Sion, vanquishing them both, the Exile reached Kreia at the core of Trayus Academy. The Exile defeats Kreia, and her plan is ended.
Just before she dies, Kreia uses the last of her powers to look into the future of the Exile, her friends, and the galaxy as a whole, she tells her what happens to everyone, and also tells her that she must follow Revan into the Unknown Regions of space. Then, the Exile either relieves her of her painful connection to the Force, which kills her (if you are Light Side), or throws her into the core of Malachor V, further feeding its dark energies (if you are Dark Side).
Kreia is easily recognizeable, with her dark brown robe always covering her whole body except the bottom of her face, as well as her missing left hand, which was severed by Darth Sion when he first attacked the Exile. Kreia has long grey hair, and her eyes are completely blank, white all the way through. She explains to the Exile that her eyes have atrophied and are no longer usable, and while she could heal them, she finds physical sight a distraction, and only sees or "feels" things directly through the Force.
Powers and Abilities
Kreia had multiple areas of expertise that were shown in KOTOR 2. She was first and foremost a historian, and therefore had extensive knowledge of ruins, artifacts, and the way the Force as a whole works.
Kreia was also a talented healer, and on multiple occasions would revive defeated enemies of the Exile and turn them to her purposes.
She had extreme power over the workings of the mind, and while she was a naturally talented manipulator, she also used the Force to confuse others, make herself invisible to them, make them forget they ever saw her, or reach into their minds and find their darkest secrets.
She also displayed tremendous power that she gained when she was Darth Traya, the two biggest weapons being her expertise at draining the life from enemies, and telekenetically controlling multiple lightsabers.
Philosophies and Teachings
Kreia, after being betrayed by both the Jedi and the Sith, held the Force as a sinister god that only could ever bring endless conflict to the galaxy. She wished to destroy it utterly. Her ultimate plan involved the Exile and his ability to make strong Force Bonds quickly. These bonds were potentially lethal, meaning that if one of the joined people die, they could all die. Kreia intented to take the Exile on a quest across the galaxy under the false idea of finding the lost Jedi, when really she was causing her to form Force Bonds with people everywhere by influencing the fates of all the planets they visited. She then planned to go to Malachor V, the site of the last great would to the force, and kill herself in such a way to generate a wound that would spread through the Exile, and then across the galaxy, destroying the Force.
She called this sort of event an "echo" through the force, where a single event could have widespread effects. The wound she wished to create would have destroyed or weakened the Force to the point where people could no longer be influenced by it.
Beyond this ideal, she was still a very manipulative and at many times mean spirited person. Part of her teachings to the Exile included a lesson on how giving aid to someone can only weaken them, by letting them not be challenged, they would not be prepared for when they found themselves alone.
Her overlying ideal, however, was that every action has consequences, some that we can predetermine and measure, and some that we can't. Because of this, every action must be thoroughly planned, and weighed against all other alternatives.