Yuki is the end result of the super-secret YLPER (similar to ESPER, short for "Ylem perception", according to the manga) Project, which attempted to create 'Esper weapons' though the use of genetic manipulation, it appears that she is one of a group of four (Lisa, Hiroko and Annie are the others). Her primary power is precognition and clairvoyance. However, as it is explained in the anime (episode XRP - 77 by the character Annie) she also possesses the power of the other three subjects, which means that she also possesses the ability to teleport things (including herself and a group of people), create force shields capable of reflecting or neutralising various attacks and cause things to explode with the power of her mind, all of these powers make her capable (as confirmed by Toru in the very last episode of the anime) of "changing the future with her own hands".
She was found by Rally Cheyenne in the street crying and was later recruited for her enormous psychic powers, Yuki is the team's 'mascot', dispatch officer and Lebia's data processing assistant. Although Yuki sometimes acts a little airheaded (she's only a teenager), she can show a great deal of courage when needed
Yuki runs a small coffee shop called Labyrinth, but it is more a hobby than a business since she is a full-time police officer. However, the lease stipulates that as long as she runs it, she doesn't have to pay rent. (It is later revealed that this is because Toru Washio, her life-long love owns the building she lives in).
She met her love interest, Toru Washio in 1997 as a result of an encounter with a Lucifer Hawk and a magical coffee mill. He was 17 at the time and she was 18. They met again after Yuki returned to her own time, 2027, Toru having waited over thirty years for her.
Towards the end of the anime it is revealed that Touru was also responsible for founding project YLPER - he had sold his soul to Nemesis so that he could see Yuki again, when he finally understood the plans that Ganossa had for Earth and Nemesis, he started the above project so that the humans "had a chance to win over the Lucifer Hawks" (episode 26).