HiMEs are young girls "chosen" by the HiME Star who are granted the ability to materialize solid objects from Photons, and the term HiME is used threefold to refer to the ability, the user and the technology itself. The term HiME is an acronym for Highly-Advanced Materializing Equipment, which could mean that HiME were not what they were originally called but are simply a more modern term that was adopted by all parties in the last HiME Festival.
Though the exact history and origins of the HiMEs are left to be speculated by the end of both My-Hime and My-Otome, various glimpses and facts can be gleamed from passing comments and information. HiME and Orphans are shown to be kept secret and covered up by First District, but the exact reasons why this is the case is never stated, it could be as a way to better control the outcome of the HiME Carnival in their favor or an order of the Obsidian Lord or for some other reason entirely, but as the HiMEs and information regarding them are scarce it seems that they have done a thorough job regardless.
What is known is that the HiMEs were originally 12 girls who fought in a battle, but whether they were fighting each other another force entirely or some combination of these (some HiME fighting for one side while others fought for the other for example) is unknown, and it can only be assumed that these original 12 even had HiME abilities in the first place. What is known is that the HiME Carnival, also translated as Hime Festival, is a "reenactment" of this first battle, (which would lead to the first of these options being the most likely) that occurs every 300 years, and that in the second-last HiME Festival Mashiro Kazahana was a HiME who was defeated in battle and held the Child Kagutsuchi. An Off hand comment by the Obsidian Lord also implies that previous HiMEs with Kagutsuchi have been rather troublesome as well implying that their were more who had Kagutsuchi and that they have been .
In episode 6 Midori is shown to be trying to investigate the history of the HiME and her research leads her to a closed off shrine
Final HiME Festival Edit
The events of which My-Hime take place cover the final HiME Festival.
Possible Relation to the Otome System Edit
In My-Otome, which serves as a spiritual successor to My-Hime there is much debate about whether or not the Otome are in someway connected or descended from the HiME powers. In the Second episode of My-Otome 0.Sifr Lena Sayers is shown with a similar mark to that of the HiME and showcases similar abilities that are more aligned with the HiME, and a book in the possession of Shiro also shows that the mark and term did indeed exist. As My-Otome is set in the distant future it certainly leaves the possibilities open, while My-Otome's two follow up OVAs Zwei and 0.Sifr leave evidence that could go either way, with Zwei seemingly indacating that the two are separate continuities while 0.Sifr implying the opposite.
Zwei showcases Childs to be completely seperate from their My-Hime Counterparts, with there being many diverse Childs who threaten to end the world as opposed to being an extention of the HiMEs, and one such Child from My-Hime Kagutsuchi is shown to be a separate entity with hostile intentions as well.
Nevertheless 0.Sifr's does canonize the HiME as being the building blocks of the Otome regardless of them being the same HiME as the ones of My-Hime or something else entirely. Lena Sayer's powers however cannot be denied as being far above that of other Otome, overloading most of the gems that she has forged a contract with and having unpredictable results in her own contract highlight these abnormalities, but her being able to materialize independently is something entirely explainable in the confines of the Otome world, but certainly plausible with the use of Eclipse1 Artemis as both the Otome Star and her child.
It is also noteworthy that in the My-Hime vs My Otome Shorts which were included in the My Otome DVDs, Arika is shown to also have limited HiME powers with a rod as her implied Element and a Child of her own, although this as canon is questionable as it was an Omake, as opposed to canon material. As both Lena and Arika are implied to be descendant of Alyssa Sears, who herself is an artificial HiME it is possible that they have this genetic potential buried within them and them becoming Otome awakened it.
As any continuation to either series has either been cancelled or was not planned at all, no definitive answer can be drawn and it could well be possible that the conflicting evidence is a result of different visions of the series on the creative teams for the OVAs, or a change in direction between the release of Zwei and 0.Sifr.