Faith(Eliza Dushku)was only on "Buffy" for a bunch of episodes on season three. We barely know anything about her past. We don't even have a last name. What we do know about her, though, is quite interesting. Faith was Kendra's replacement as the second Vampire Slayer. Unlike Kendra, she leads a social life, so slaying isn't all there is for her. But like Kendra, she's proud of what she does and loves it. From her attitude and way of life, we get the idea that she had problems in her family while growing up.
She first showed up in the episode "Faith, Hope, and Trick." Buffy spots her leaving the Bronze with a vampire and goes to rescue her... only to find her already fighting the vampire herself. After that, Joyce invites her to dinner and Faith starts hanging out with Buffy's friends, and no one seems to pay attention, so she goes through a small period of jealously. She gets over it, and they pretty much become friends.
In the episode "Bad Girls," Faith accidentally kills the Mayor's main helper when she mistook him for a vampire. Things go downhill from there. Faith shows no remorse for what she did, while Buffy feels terrible about it. They find Faith, tie her up, and Angel tries to talk to her about what happened. But Wesley had overheard Buffy and Giles talking about what Faith did, and he informs the Watcher's Council about it. They go to Angel, knock him out, and arrest Faith. She managed to get out while on the van. At the end of the episode, she goes to the Mayor and informs him that she will be joining his side.
Apparently, by the next episode, "Enemies," the gang starts to suspect that something is wrong with Faith, because they set up a plan. Faith and Mayor Wilkins had been trying to get Angel to lose his soul. When Faith found that she couldn't seduce him, they turned to a sourcerer to do the job by magic. The sourcerer happened to be a friend of Giles' who owed him a favor, so he simply pretended to take Angel's soul away. By acting as a spy, Angel discovers some of Wilkins' and Faith's plan.
After that, in "Graduation part 1," Faith shot Angel with an arrow that had poison that could kill a vampire. The only thing that could cure it was the Slayer's blood, so Buffy went after Faith. They fought, and Buffy stabbed Faith with a knife, but Faith jumped off the building and unto a truck that was passing by. She has been unconscious ever since.
There are things that happen in between all of this, like the fact that the reason Faith was in Sunnydale in the first place was because she was being chased by a demon name Kikistos(which she and Buffy killed), who killed her Watcher. And of course, her little tyrst with Xander in "The Zeppo." Faith is pretty much a 'have fun' type of person. She doesn't go to school, she sleeps with guys just for fun, she's not too sensitive and never really understood Buffy and Angel's relationship.