Holy Grail

The cup that received the blood of God.
It is one of the greatest holy relics, a wish-granter that fulfills its owner’s desires.
It is believed to have its origins in the “wish-granting cauldron” that appears in numerous myths.
The Holy Grail that appears in Fate/stay night is not the original, but rather a replica made to function as a “wish-granter.”
When Heroic Spirits are defeated, they return to their original forms as fragments of power and vanish from the time axis.
However, before that can happen the Einzbern Holy Grail intercepts and stores them until the ritual to open the “hole” can be enacted by the Great Holy Grail.

Fate/side material: Fate Encyclopedia

A miraculous wish-granting machine that can grant any wish. The Holy Grail was created 200 years ago by the Three Founding Families. It has its origins as the “wish-granting cauldron” that appears in numerous myths and legends. The Holy Grail that appears in the Fuyuki Holy Grail War is not the original, but rather a replica made to function only as a wish-granting machine.

Fate/Zero Animation Guide I: Glossary of the holy grail war I

In previous works the term Holy Grail referred to a wish granting machine that could grant any wish, but in EXTRA this term refers to the right to use Moon Cell.
If you browse through the massive amount of records and simulated data that Moon Cell holds, you will certainly be able to find a version of Earth with the future that you desire.
The you who has obtained the right to use Moon Cell need only say the following to Moon Cell:
“Recreate my ideal future.”
Moon Cell will quickly set about to bring the state of Earth to match the shape of the future you desire. The Moon has all the necessary knowledge and physical means to change the world.
For example, if you were to wish “Make all the girls on Earth my little sisters.” In about ten years or so societies on Earth would have changed to be so.
Or alternatively, all of Earth would be managed and directed to work in order to make a device to allow one to experience that dream realistically.
There’s nothing that the human race can’t realize as long as it’s within the scope of human imagination. No matter what kind of fantasy, no matter how unrealistic, there is a way to realize and experience it.

Fate/EXTRA Material: Encyclopedia of Fate/EXTRA