Pandora was not her original name, but in fact, the name of the Pithos she was meant to open. She began using that name after being called that by a time-traveling Illya.
Pandora was created by the Twelve Olympians six thousand years before the events of PRISMA☆ILLYA. Differing from other worlds, Pandora's Box was never opened in Miyu's World, so Pandora was left unable to die because her "death" itself is also within the box. She was given knowledge by the gods that she had to wait until humanity perished so that she can finally open the box and release the world's true potential. Because of her immortality, Pandora suffered greatly as people unreasonably tried to kill the undying mud doll whenever they discovered she wasn't human. After so many years of suffering, Pandora began questioning on why she had to go through this for humans.
Having been found by Darius Ainsworth one thousand years before the events of PRISMA☆ILLYA, Pandora has lived with the Ainsworths since then. She has taken on various names over the generations, the most recent being Erika.
Erika is a child that is seemingly full of innocence that is always cheerful, though has a strange tendency to lie a lot. It is unknown if she really understands what is going on around her, however she does understand her adoptive father, Darius Ainsworth, to a certain extent. One example was how Erika understood that Darius Ainsworth would disapprove of her bringing Illya to the Ainsworth's castle unless Illya was reduced into a powerless state which prompted Erika transfer Illya's soul into a stuffed animal. Although she originally wanted to brainwash Illyasveil von Einzbern, she chose an alternative where she is still apparently pleased. Despite this, Erika seems to genuinely love her "older sister," Miyu Edelfelt, as she seemed to be really lonely as Miyu was gone in a parallel world.
Overall, she can be similar to Illya's Fate/stay night counterpart, as Illya describes Erika as a "twisted child" whose innocence can fool people into thinking that Erika is harmless when she really has a cunning side of her that can potentially make her very dangerous; however, she is indeed a child that is afraid to be alone and tries to use any method, albeit rough, to avoid being lonely. All this accumulates on how she has the naive mind of a child that lacks moral and common sense, especially when it comes to other people's lives.
After Erika reawakens as Pandora, her personality shifts dramatically; her true mindset is that of a cold and disillusioned being, similar to her brother Julian Ainsworth. 6,000 years of abuse from humanity have caused Pandora to develop a deep-seated hatred for the human race, and her only desire is to be killed so that she can be relieved of her duty to open her box. It is unclear if her childish persona is an act or not, but these sharp personality shifts between a cheerful child and a despondent death-seeker have happened for as long as she's been with Darius, triggered whenever something reminds her of her loathing for humans.
During the decline of the Age of Gods, Pandora acted like a proud individual who asked not to be compared with the other members of the human race. Although this was a front for the fact that she was actually a lonely person who didn't have a single friend.
Fate/kaleid liner PRISMA☆ILLYA 3rei!!
Introduced as having stumbled on Illya and company's temporary school hideout (and not triggering the alarm system, which was designed to respond to hostile intent), she quickly befriends Illya, who believes she is an innocuous inhabitant of the alternate Fuyuki City. Having played off of Illya's desire to be a big sister, she is given shelter at the hideout for the day until her father comes to retrieve her. During their reunion however, Illya fixes the alarm system, which immediately sounds the alarm on the intruder; Illya quickly realizes Erika is the daughter of Darius Ainsworth. During this encounter, Erika's dubious innocence is a source of unease to all present except for Darius himself. Her real reason for sniffing out the hideout was to learn what kind of person Illya is, having heard about her from the captive Miyu.
The night following the confrontation, in contrast to her seemingly short stature and allegiance to the Ainsworths, Erika manages to abduct Illya in her sleep (once again not triggering the alarm). Her reasons for doing so were in the hopes that Illya's presence would improve Miyu's mood, but recognizing that Illya was an enemy, she tried various methods to make her docile, first by having her brainwashed, and by then having her soul extracted. Not only is Miyu mortified at what Erika did, Illya proves to be more tenacious than she expected as both curses failed, and she eventually reunites with a captive Kaleidostick Magical Sapphire that allows her to transform and rebel against her captors. The chaos that ensues because of Erika's blunder infuriates Darius, who gives her a harsh spanking as punishment.
In the following battle, after Miyu is freed and reunited with her Kaleidostick, Miyu hesitantly informs Erika that because they are on opposing sides of a conflict, they cannot be friends. This triggers a mental breakdown in Erika, enhanced by the appearance of the mysterious "mud cube" that douses her shortly after, suddenly giving her a body slightly shorter but seemingly older than Illya. After Miyu is temporarily recaptured in the struggle, she and Julian attempt to open the cube, but fail - Gilgamesh informs them that a single Holy Grail (Miyu's true nature) is not enough. Before they can act on this information however, Tanaka throws Illya a mysterious flaming sword that allows her to destroy the mud and damage the box, forcing the Ainsworths to retreat.
Later, after Illya chases a manic Tanaka around Fuyuki City, they come across the school that they have since abandoned as a hideout, finding the now-older Erika there once again. Now displaying a completely different personality than before, Erika asks Illya if she wants to save her - and the points out that this means Illya would have to kill her, because her only wish is to die. A mortified Illya cannot respond, but Tanaka defuses the situation. Julian retrieves Erika with Displacement Magecraft before things can escalate any further.
After Illya and friends piece together that the giant "mud cube" Erika wields is Pandora's Box and believe she is using the Class Card "Pandora", Julian unleashes said box over Fuyuki City the following day to lure Illya and Miyu out for their final confrontation. Though a resurrected and berserk Sakura Matou is dispatched to keep Miyu and Chloe von Einzbern out of the fight between Julian and Illya, they reach Julian first, necessitating Darius to intervene. The girls are subdued, whereupon Pandora abducts them into some sort of abstract space where she is upside-down.
As the three girls talk and Illya fights Julian outside, Erika's true nature and origins are revealed. "Erika" is not her real name and is in fact just one of many aliases she assumed over her time with Darius, and she is not using the Pandora Class Card - she is Pandora, the first human created by the Greek Gods 6,000 years ago, tasked with opening her box on the day humanity goes extinct. In Miyu's alternate world and in an alternate retelling of the original myth of Pandora's Box, this Pandora was not overcome by curiosity and did not peek inside the box, and is effectively immortal until the box is opened because it contains her concept of death. Unfortunately, her immortal nature resulted in her being labelled a monster by humanity, resulting in 6,000 years of suffering and agony.
Pandora recounts that her only wish at this point is to die and be relieved of her endless duty, having no love for humanity after her treatment at their hands. Miyu, however, rebukes that even if Pandora is not a true Ainsworth, she has certainly picked up their habit of chronic lying, and argues that Pandora is hiding her real wish and refuses to use her power as a Holy Grail to grant a fake wish. Miyu then asks what her true wish is.
After Julian is defeated and the mysterious space shattered by the combined efforts of Illya, Miyu and Chloe, it is revealed that the space was inside the giant cube - and also that the cube is not the true form of Pandora's Box, but rather a black hole inside the cube that is spewing the corruptive mud, described by Julian as "a world's worth of ruined possibilities". A resigned Pandora comforts Julian in his moment of defeat, only to be mortally wounded (but not dead as the Pithos remains unopened) as Darius assumes full control of his body for the final battle.
Following the battle, Darius succeeded in forcing Pandora's Box open, covering the entire world in its mud and ending human civilization. However, a flaw in the plan was encountered after the fact: the box cannot fully empty until all human life in the world is extinct. With Illya having been saved by Gilgamesh, and Pandora unable to die until the box is fully opened, two "observers" of human history still remains, and thus Darius' plans for the box are halted as he is frozen in time only a moment from victory. This results in Pandora's concept of death still staying inside of the pithos, and she remains incapacitated and lost in the destroyed world.
Pandora possesses the Noble Phantasm Pandora's Box where she is its key to opening it, but she initially refuses to open it because of the duty that was given to her by the gods. Until she does, she is unable to be killed or permanently injured, making her immortal. She can control the corruptive mud the box produces and summon Blackened Heroic Spirits from it. She can also create a sturdy, pyramid-shaped barrier to defend herself.
Based in the legend of Illya's World, Pandora presumably had the ability to open Pandora's Box during the time when she was created. However, after living for so long and suffering so much trauma to her pysche, she lost some of the functions to act as a proper key for the box, an error so extreme that only a powered Holy Grail can correct it.
Pandora has been subject to having her soul and consciousness displaced for over 1000 years, as Darius states that although her body is immortal, her soul gets worn down by the passage of time. So Darius uses it to have Pandora "spit out all her soul" as a pool of black mud or "pus", getting rid of the "intellect" of her broken mind and "resetting" her personality and memories, reverting her physically and mentally into the body of a "ignorant and innocent child" so she would not suffer suicidal despair at her undying condition. Darius then stores the data of her memories and body within the Pithos, and will reset her again the next time she gets to this point of begging for death and uselessly trying to kill herself.