Along with several other Cores, Miku was built and programmed by Crypton Science to serve as a distraction to KaITO and hopefully prevent (or at least, slow down) any murderous rampages.
It didn't work and eventually, KaITO just vanished, having somehow found his way into the DR.
So, Miku was left to her own devices so to speak and set about collecting information to pass on to KaITO once she managed to find him. This has resulted in two hundred year's worth of knowledge sitting in Miku's head, waiting to be used. Unfortunately, she's too much of a ditz to use any of it practically. Eventually, Miku found her way into the DR as well and by chance, ended up encountering KaITO again. Now she's tasked with keeping an eye on the other Cores and reporting back if anything happens.
Canon Information Edit
Physical Statistics: Miku is your average Hatsune Miku, save for a few differences. For one, she's a lot bluer than most other Mikus -- while they tend to be on varying shades of the teal scale, Miku's main colour is turquoise, with hints of a deep, royal blue. In place of the usual red 01 stamp on her arm is a logo that reads 'Crypton Industries' and the 'VOCALOID' under the yellow label on her shirt now reads 'C-CORE'.
Personality: Miku serves as a 'Curiosity' core, a robot whose purpose is to endlessly ask questions and seek out information. As such, she'd acquired quite a wealth of information; unfortunately, she's not quite managed to pick up common sense yet. She can spout off pi to a thousand places on a whim but she's much too ditzy to put any of her knowledge to any real use. However, collecting information is not Miku's only purpose -- in fact, it's not even her main purpose. Miku's main function is to serve as a distraction for KaITO to preventing for murdering everyone in the Crypton Enrichment Center. She does this by relaying as much of her information to him as she can. As such, she's programmed to be 'attached' to him and while she can recognize that he might not be entirely right in the head, she'll still naturally gravitate towards him in most situations.
In order to make people more inclined to answer her questions -- and therefore, to help her gather information faster -- Miku was given a purposely childish personality. The reasoning for such was that children always ask questions, so why not make her act childish? Of course, the problems with this are countless but Crypton Enrichment weren't very well known for their common sense either, so Miku became a playful, endlessly curious, cheerful and ditzy young girl.
Abilities/Powers: Has access to mountains of knowledge and trivia and possesses some knowledge of robotics. She's also a novice at computer programming.
Strengths: Intelligent, intuitive, remains safely operational at temperatures up to 4000 degrees kelvin. Lacks the vulnerabilities of a human body. Also, SCIENCE.
Weaknesses: Lacks common sense, can be destroyed easily if you know how, susceptible to computer viruses and the like. Has to follow KaITO's orders, no matter what they may be.