Nobody really knows. There are mystery characters in Bleach and that makes it awesome for imagination and infinite possibilities and probabilities! :)
- They are perfectly normal children… with superpowers.
I suppose it’s possible that Ururu and Jinta are just normal kids - orphans, perhaps, that Urahara kindly adopted. They do age, after all, and it’s not like we don’t have plenty of examples of humans who have super powers. There would still be a question of how they got super powers, of course - and presumably Urahara had something to do with that.
- They are constructs.
Much more likely, to my mind, is that Ururu and Jinta are artificial children created by Urahara. This would explain their super powers, where they came from, and why Ururu has Urahara’s hair. Plus it’s Urahara. We know that he’s something of a mad scientist.
- Jinta is normal; Ururu is a construct.
A third possibility is that only Ururu is a construct, and Jinta is a normal(ish) human kid. Ururu has done a lot more to be suspicious about - like when she fought Ichigo with so much power that he ran for his life. Or when she struck an Arrancar hard enough to make him bleed. Jinta has a bat that he can swing pretty hard, but he hasn’t done anything quite as extraordinary as Ururu. So perhaps she is the only construct.
- They were created to fight Hollows.
Of course, whether Ururu and Jinta are constructs or whether they are humans with powers, the question still remains - why did Urahara make / empower them? One idea is that they were created as a weapon against Hollows. That would explain, for instance, why Ururu lost it when Yylfordt appeared and went into “Genocide Mode.” Because having a Hollow around made her, um, circuits react.
- They were created to fight the Quincy.
There has been no indication that this is the case. I mention it merely because, since we are now in Bleach’s last arc, all the reveals that are going to happen need to happen in a Quincy context. So perhaps Tite Kubo has saved the reveal of Ururu’s and Jinta’s true natures because they were actually created as some sort of weapon against the Quincy. Urahara is a guy who likes to plan ahead, after all.
- They are the shop’s defense mechanism.
Or perhaps Ururu and Jinta weren’t created to fight any specific enemy; perhaps they simply constitute the shop’s defenses. After all, what Ururu reacted to when it came to Yylfordt was his unusual spiritual pressure - a reaction that makes sense if she exists to guard the shop against hostile intruders. And for a man like Urahara, on the run from Soul Society with a shop full of dangerous (and only dubiously legal) items, having a defense team makes sense. Why he decided to make ‘em kids is an open question.
- They are replacements for children Yoruichi and Urahara couldn’t have.
This, at least, is the theory that the anon sent me along with the request. Apparently one theory is that Yoruichi either had a miscarriage or simply couldn’t have children, and so Urahara created these replacements. I have my doubts about this one, insofar as it seems dangerously shippy for Bleach (a canon couple with both characters living? What?), and also Yoruichi has shown no particular affection for the two kids. But it’s a possibility.
- They are mod souls.
Now that Ururu and Jinta have aged, this may be unlikely but hey. Maybe Gigais that age are a thing now. After all, we’ve so far had only one mod soul in canon - Kon. And what we know about the mod souls is that they were created to fight, and they were given specific offensive powers (Kon’s seems to be “kicking”). Kon himself came from Urahara’s shop - from a box of “defective” merchandise. So if Urahara had one mod soul, why not more? Perhaps Ururu and Jinta are both mod souls that Urahara rescued, and that explains their powers to fight Hollows.
- They were created by the Hogyoku.
We’ve seen new life created in a couple of ways in Bleach. There’s Kurotsuchi’s creation of Nemu, which seems to be tied to whatever the hell Kurotsuchi is, and there was Aizen’s creation of Wonderweiss, through the Hogyoku. Well, we know that Urahara also had the Hogyoku for a while, and we know that the Hogyoku manifests desires. So perhaps Urahara said to himself, “Man, I wish I had a couple of kids who happened to be awesome at fighting Hollows” and the Hogyoku took care of the rest.
- Tessai created them.
Or perhaps I am way off base to think that Urahara created them at all. There is another guy in the shop, after all, and Tessai’s abilities are as mysterious as his past. All we know is that he’s a genius with Kido, and he works with Urahara. Maybe he’s the guy who created Ururu and Jinta, using his Kido experience. Can Kido even be used that way? Probably not....
And I saw a cool theory that Ururu and Jinta are mod souls based off Rukia and Renji, and then placed in a Gigai which slowly bonds with the soul inside it. Rukia's Gigai was going to turn her into a human if she was left in it long enough, which explains why Ururu and Jinta age like humans.
Them having totally different personalities from Renji and Rukia is weird, but look at Nemu and Mayuri.