*The origins of Einzbern
A factory originally created by the students of the magician who realized the third magic. Began in the year 1 AD.
They attempted to reproduce their master's miracle, but couldn't do it themselves, so as an alternate plan they tried to recreate a specimen identical to their master and have it reproduce the magic.

After nearly 900 years of effort, Justeaze - the homunculus who would come to be called the Winter Saint - was forged.
She was a model that strayed from what the magi had intended, created completely by accident, but her abilities were equal to or above those of their master.
The magi should have been elated about Justeaze, but they couldn't be happy. After all, she was a mutation that was born regardless of their own techniques or skills.
Even if that specimen was to reproduce the third magic, that conclusion would be harder for them to bear than 900 years of failure.

The magi deperately attempted to create a homunculus that excelled Justeaze by their own techniques.
The artificial intelligence created to act as the castle's central management - the golem Jubstacheit - was the pinnacle of their craft, and became the father of all homunculi created at Einzbern.

Justeaze succeeded at proving the third magic.
However, it was not cost-effective. Justeaze's use of the third magic was like careful knitting. It would take several years to save just one person, making the salvation of the entire human race virtually unattainable.
In addition, while Justeaze herself did not age, her body was so frail it would take little to kill her, so she could not leave the castle.
Since her intelligence and mentality were also unaging, she did not develop at all. From an outside perspective, it was as if she was repeating a single day for all eternity.
If she were to leave the castle she would be freed from this "single day", but the act of leaving the castle signified an easy death for Justeaze.

In the end, they accepted that humans could create something that surpassed humans, but not something that could save humans.
...Or perhaps they would not have failed if a miracle like Justeaze had not occurred.

The magi despaired the limits of their abilties. Some abandoned the castle, while others took their own lives.
The homunculi left at Einzbern were abandoned by their creators, but in their purity, they continued to operate the factory for the sake of the creators' ideaology - the salvation of humankind, the reproduction of a miracle.

From then on, all homunculi created at Einzbern were based off of Justeaze.
Jubstacheit created a humanoid terminal unit, and used it as the manager of Einzbern. Though by the end he operated even Acht (the eighth humanoid terminal), he did not possess a personality.
He only included the necessary "humanity" to operate the castle and reproduce the third magic into each of his humanoid terminals, and made them act like humans.
Jubstacheit is essentially an automaton that cannot progress, but continues operating in perpetuity. His way of existence is just like an old clock ticking away, being forgotten by people before running down.

*The great grail
Five hundred years after the magi departed from Einzbern, a model plan was devised for a wide-area operation device for the third magic using Justeaze.
Einzbern had determined that reproducing Justeaze was impossible.
Their plan of keeping Justeaze safe because she was a unique and valuable model switched to a plan to use that unique model to mass-produce miracles.
(This was not Jubstacheit's plan, but a consensus of opinion within Einzbern. Because the homunculi were pure, they chose the method with the greatest probability of success. In fact, Jubstacheit was the only intelligence that voted against this.)

Justeaze could only use the third magic on one human over a period of decades. Therefore, using Justeaze as a frame, they would create a "greater" magic formula and save many humans at once.
The plan was to disassemble her magic circuits and replace them with a magic formula, creating a humanoid universe - the great grail.

But Einzbern alone could not start this project.
They were no more than dolls. They had no way to live in the outside world, and they couldn't handle the complexity of human society.
To create the great grail and reproduce the third magic, they needed understanding and cooperative humans.

Then, in the year 1800, a guest arrived at the winter castle that had continued to produce homunculi.
Makiri Zolken. A magus who had devoted his life to eliminating all the evils of the world, the evils of humanity.
(At this point, Zolken was mostly disillusoned. He knew it was about time to give up, but calling on Einzbern was his last hope. He met Justeaze, and felt a complicated mix of emotions - hope towards fulfilling his ambition, jealousy at her ability to use the third magic, and pity for Justeaze's eternal youth causing her to "repeat the same day".)

With Makiri's understanding and Tohsaka's cooperation, Einzbern began to create the great grail.
However, once they started, they determined that Justeaze alone was not enough.
They could create a great grail. They could create its core. However, to operate it they would need vast amounts of magical energy, and a lesser grail to control it.
Makiri and Tohsaka devised a ritual to collect magical energy using Justeaze's ability to connect with the root: the grail war.
Despite being unable to reproduce Justeaze, Einzbern created a lesser grail with similar abilities to hers.

After 10 years, the project was finally complete.
The grail war ritual was successful, and the great grail lit up.
But its first operation ended in dismal failure.
There was no flaw in the great grail itself.
The problem lay in the craftsmen and magi who participated.
Instead of using the precious magic reactor core for the sake of the whole planet, the magi killed each other out of a desire to use it for the sake of their own race or society.
Einzbern had been unable to understand the thought processes of the humans who operated the great grail.

*Irisviel and Illyasviel
Einzbern learned from the failure of the grail war and changed their plans.
Justeaze no longer existed.
While preparing to restart the great grail, they returned to their original goal and focused on creating a perfect homunculus.

As a result, they created Irisviel, a homunculus with the function of a lesser grail. They expanded on her further and Illyasviel, a homunculus that was the pinnacle of Einzbern's technique, was born.

*Tuners
This is a digression, but separate from the winter castle is the tuners' building (a small house), inhabited by a family of human magi, not homunculi.
Since the homunculi cannot negotiate with human society, the tuners went into town in their place and barter for needed materials. Traders, essentially.
Still, they are a talented magus family, and possess strong artistry. Humans without strong aesthetic sense could never take care of Einzbern, after all.
The tuner family's numbers dwindled along with Einzbern's decline, and in the end only one remained.
It seems he often worked in the castle as a butler, teaching the secluded, medieval-minded homunculi about the outside world.

It's unknown what kind of conclusion that tuner chose after Illya lost and Jubstacheit shut himself down.

*In summary: so what is Einzbern?
A factory in which homunculi continued operating towards the ideals and goals humans had given them, after the magi had left.
Jubstacheit is something like the factory's central management program. A monolith. Acht is his terminal.
Even after their creators had given up and died, the homunculi in the winter castle devoted themselves to making their masters' dream come true.

What lies at the basis of the Einzbern factory and many discarded things is the purity of machines.
Imagine a doll that can speak to its owner, but only a few phrases.
"Hello", "thank you", "I'm sorry", "good night" - "I love you."
These reactions delight the buyer, but it's clear that they will soon be disappointed.

"No matter what I say, the doll can only say predetermined phrases. It just keeps repeating that tired old 'I love you'."
Realizing that the love the doll speaks of is a false emotion, the buyer will likely discard it eventually.
But humans are the ones who see that as empty words and a manufactured fake.
Even if it doesn't have a "heart", even if it's only repeating the same words, there are no lies in the actions of machines.
They innocently carry out the task they were given.
"I love you."
Though abandoned, forgotten, and scorned as out-of-date dolls, they continue to carry out their mission, unchanged from the time they were designed.
Machines do not lose their worth when a newer model appears.
Their worth (life) ends when humans can no longer bear that purity.