Kyo has descended from a long, powerful bloodline, known as the Blackbloods. They're very rare, they've been given this infamous name because these 'Blackbloods' just faded away into mere darkness. It's like they've been wiped off the earth completely, no one has heard of them in centuries.
Now this bloodline allows one to be bitten by a pureblood, but will not turn into a vampire. So, naturally most of these race of people pursued the occupation to become vampire hunters. Kyo's parents were vampire hunters, but Kyo does not know that. She was adopted at a young age by none other than Kaien Cross. Her parents gave her up because they knew that purebloods from all ends of creation would come looking for her craving for blood.
[EDIT: I MADE THIS IN LIKE 6TH GRADE- WHY DO YOU GUYS STILL READ THIS ASKDLSK-]