The Exile (who is canonically female, so I will refer to her as such) does know a lot of things you do not, however, which is one of the reasons the story is so praised; this game managed to give us a PC who HAS a past that is not explained by cutscenes and flashbacks (save one), but rather we piece it together from her interactions with others.
In addition to that, the game is REALLY about the Mandalorian Wars, which took place 10 years earlier, and again, it manages to be about that without flashbacks.
Anyway, here's the Exile's backstory, as pieced together through the game: she was a young Jedi when the Mandalorian Wars started, and she decided (for reasons that the player chooses in the present day when she talks about it, that's what I meant by being about 10 years ago without flashbacks) to defy the Council and join Revan to fight against the Mandalorians. Eventually, she became a General because of her ability to inspire her underlings (which will be VERY important later).
Anyway, because of the horrors of the last battle of the war, Malachor V, and because she lost her connection to the Force (and, it is implied, because Revan manipulated her into doing so), the Exile was the only Jedi to return to the Council to face judgement. They decided to exile her, hence her name.
She wandered around the galaxy, missing the events of the first game entirely, until eventually (and we aren't really told why), the Exile decides to return to civilization, and was going to Telos aboard the Republic ship Harbinger when certain events happened which end with the Exile being on Peragus, the first level of the game. I won't go into too much detail, but basically: Sith want the Exile dead, the Exchange wants to capture her, and Kreia wants the Exile alive for her own reasons...
Now is probably a good time to discuss what we find out when we find the Jedi Masters (assuming we do it the Light Side way and do not kill them). We're told that the Exile always created Force Bonds with others, unintentionally. These bonds were VERY strong (hence the fact that she could feel Kreia's pain when her hand was cut off) and were created VERY quickly. While she was a General, she created thousands of these bonds. And then, at Malachor V, all those bonds were violently cut off at the same time. So she had to cut herself off from the force or she would have died. This somehow damaged the Force itself; the Exile became a hole, a "wound" in the force, but she didn't stop creating those bonds. In fact, the bonding got even stronger, The Exile basically became a Force black hole; she created those bonds and used the Force through others.
Now for Kreia's motivations. Kreia hates the Jedi Council, but she does not want them dead. Basically, Kreia had some interesting beliefs that the Jedi did not share. She believed, among other things, in moral relativism, and disliked both the pure light side and the pure dark side. She preached balance, essentially (She also hated the Force itself, but more on that later). However, every student she ever had (including, it is revealed, Revan) turned to the Dark Side, and eventually she was shunned by the Council. She decided she wanted revenge. Not, in a refreshing change of pace, by killing them, but rather by showing them how wrong they were. So, she finds the Exile (who is dead to the force, which interests her for other reasons) and decides to train her. She also tells The Exile one, simple lie: The Council is the reason you were cut off from the Force. She did this so the Exile would find the Council members and get them all to meet up, which is exactly what happens if you are light side.
When you are light side, you meet the council. This should be Kreia's moment of triumph, but the Council was blind. You know what, I'm gonna quote a certain LP [http://lparchive.org/Knights-of-the-Old-Republic-II/] here. This guy explains it really well:
"Kreia gathered the Jedi Masters here for a purpose: revenge. But for her, revenge didn?t mean killing them. If the Exile had gone Dark Side and fought each of the Jedi Masters, Kreia would have berated him for being such a murderous idiot and not learning anything from her.
Kreia was cast out of the Jedi Order for her beliefs. The council disagreed with her teachings, and the fact that most of her students ended up going all evil and whatnot didn?t exactly help her case. All this time in exile, she schemed to find a way to get back at them, to show them the error of their ways. For her, victory would have been the Jedi Council admitting they were wrong.
She never intended to kill them, since it would have been a hollow victory that way. But they were stubborn idiots and they forced her to act. That?s why she sounds so regretful here."
That was Kreia's motivation for most of the game. After the Council dies, she sort of BSODs and something...different happens.
Throughout the entire game, there had been an undercurrent in the dialogue with Kreia: she was all for everyone's freedom to choose. And yet, there exists the Force, which controls everything and seems to have a will of it's own. Kreia HATES this idea, that there can be this omniscient force whose will supersedes all others. That was the other reason Kreia sought out the Exile: she was the only person in the galaxy who was completely free of the Force, and Kreia loved her for that.
Again, the LPer sums it up well:
"Star Wars has more similarities to Tolkien and high fantasy than most sci-fi franchises, and one of the most telling aspects of it is that you have destiny disguised as the Force. Everyone keeps saying the Force guides all things, trust the Force, etc. Then you you take a control-freak like Kreia who values self-determination above all else, yet who uses the Force as well, and suddenly you have this fate vs. free will dichotomy manifested within the same character."
This part is actually quite hard to explain, so I will just link [http://lparchive.org/Knights-of-the-Old-Republic-II/Update%2059/] to the page in the LP that covers this part.
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