Little is known about Kendra. It is presumed that she is from Jamacia (from her accent) but there is nothing to back this presumption up. Her Watcher is called Sam Zabuto (Giles has heard of him), and Kendra's parent sent her to him from a very early age. (she has seen pictures of them.)
She couldn't be any more different to Buffy. She knows the ancient texts of lore, reads form the Slayer's Handbook and has been much more severely trained than Buffy. She doesn't have any friends other than her Watcher and her she seems to have only one set of clothes. Kendra never went to school, she was taught by her Watcher. She is much more secretive about her 'job' than Buffy. She hitched a ride to Sunnydale in the bagage hold of an airplane, and more whimisical than Buffy as well, she has a name for her favourite stake (Mr Pointy).
It's quite obvious that she does not approve of the way Buffy works as a Slayer, she tells her that it isn't a job, it is who you are.
Kendra became the Slayer after Buffy was killed in 'Prophecy Girl', it seems it doesn't matter how long a Slayer is dead for before the next is called.
Her Watcher discovered what Spike was trying to do when he stole the du Lac cross and sent Kendra to put a stop to it. However, her arrival in Sunnydale did have a few problems. She locked Angel in a storage cage and left him to burn and she tried to kill Buffy because she saw her kissing Angel. Once all this was sorted out things got better. (even though Angel was in Spike's clutches.)
Once Spike's plans were foiled though, Kendra returned to where she came from, this time travelling in the passenger compartment of the plane.
When the world was in danger again, this time from Angelus and Acathla, Kendra returned to Sunnydale to help Buffy out. Buffy got her to stay in the library with the others while she went to meet Angelus. However, it was all an elaborate ambush and the only protection the Slayerettes had from Dru and her henchvamps was Kendra.
Unfortunately, Drusilla had a trick up her sleeve and managed to hypnotise Kendra before useing her nails to slit her throat. When Buffy got back to the library she found Kendra lying dead in a pool of blood. Another Slayer had met her inevitable destiny.