Kobato has a mission to fill a mysterious bottle with people's healed hearts. However, it wasn't explained in the anime as to why she has this mission or her origin. Wikipedia doesn't seem to know anything about it as well so I'm curious if CLAMP ever mentioned her story before she came collecting jar of hearts and why she had that wish to go to a certain place. Or was her story featured in any of the CLAMP's multiverse or in the manga?
Ooops.. Sorry my bad. I was too lazy to read the whole page when it already contained the answer.. :P
At the conclusion of the anime, it is revealed that Kobato died in the distant past. She exists in a liminal state where she neither dead nor alive. In the end, when she finally fulfills her task to fill the flask, she is reborn without any memories of her past life until she meets Fujimoto again few years later. In the manga, it is revealed that Kobato had died due to the war caused by Ioryogi and the gods. The angel that Ioryogi had fallen in love with felt pity for the girl who died before her time was up and transferred her soul into Kobato, being able to since they both have the same soul but belong to different worlds. The time limit Kobato has is the time before the angel disappears.