OJ Simpson had three lawyers--"the dream team." One of them was Robert Kardashian, father of Kim. Her parents divorced when Kim was young and Robert died in 2003. Her mother has been married to famous Olympic athlete Bruce Jenner since 1991.
Kim is mostly famous for being the best friend of Paris Hilton and for this sex tape made with rapper Ray J, who is the brother of the singer/actress Brandy. Both Paris and Kim are self-absorbed party girls who seem to have no claim to fame other than their social lives and sex tapes. Kim is also the main star of a "reality" show on the E! channel called "Keeping up the Kardashians" that follows the adventures of her family.
Oh, and she isn't at all Indian. Her unusual name and perhaps exotic look comes from her father's Armenian ancestry. You can read all about her on Wikipedia.