Story
It's hard to explain the tale when not every detail had been given. We know, for sure, than one day four travelers from different worlds arrived at the Witch of Dimension's shop. Three of them had a wish that involved crossing through space-time. The Witch, known as Yuuko Ichihara, asked her young assistant to go to her "treasure cove" and get her two furry animals that were sleeping in glass bells. One was white, one was black.
The visitors paid Yuuko's price with their most precious things. The result of the sacrifice was her giving them the white creature; the black one would stay with her and work in communication. The white one could be a way of interdimensional transportation. So they left, although it wasn't the end of the story.
That's the Tsubasa RESERVoir CHRoNiCLE premise. But as it's not the end, it's not the beginning either. Yuuko would tell Kimihiro, the assistant, at least a part of the story in the second XXXHOLiC volume.
Long time ago, Yuuko had found a white creature like those ones, once, a creature from a different dimension. "It had created a world and went through a journey to create another one [...] I found that white, rounded little thing, that looked like a manjuu. Actually,
we found it."
At that moment, she was in company of a sorcerer called Clow Reed. What we don't know is if their encounter with the godlike creature was accidental or intentional, and if the plans they developed beforehand or because of that meeting (in the lines of 'hey, I have an idea; we can do this and that to help those kids!') I like to think they both had a detailed deal beforehand, and their investigation and powers leaded them to find the original Mokona, the world creator.
The point is, after they had met Mokona, they knew how to do things. "Together we made these two beings from another world... For the time that pair of persons that are Clow's relatives, but at the same time aren't, arrived here. [...] So we made those little ones to give them to Syaoran and Sakura, that came from another world. And for the other two who were going to need them."
Basically, Clow and Yuuko knew those kids were going to need a way to travel through dimensions, and they'd come one day to Yuuko's shop. So, with years in advance, they prepared themselves and created two clones of Mokona, with abilities they were going to need. After they trained Mokona Modoki, they sealed them in those bells, and Yuuko waited for the moment. Clow would already be long time dead by then.
We know Clow had motives for helping the visitors, as in Yuuko's world Sakura and Syaoran are his relatives (and actually, in their own world, the girl's not far away from the family tree...) But what about Yuuko? Why did she ally herself with the famous magician? Is it because they were friends? Is it because they're future clients and she was going to need help to grant their wishes anyway? Is it because Clow's also a client himself, he asked her to help the unborn kids that day, and he gave her something in return for her services? Is it because the one who plotted the tragedy upon the kid's country, who's also related to Clow, is a common rival and we didn't know? Or is it because creating Mokona Modoki will also help her in her own plotting for something entirely different (ie, black Mokona -Larg- saved Kimihiro Watanuki's life in a couple of occasions, so maybe helping Watanuki and granting his wish was part of the big plan)? Or is it several of the above? We still don't know the answer, or if there's more than one.
If you're interested in the backstory time when Mokona Modoki were trained by the two powerful sorcerers, then check the translations section.