Holy Grail War

A term for a competition to acquire the Holy Grail.
So long as the prize has the same abilities as the Holy Grail of legend, even a battle for a fake will be deemed a Holy Grail War.
However, the Fuyuki Holy Grail War is particularly special, as the Servant System that turns Heroic Spirits into familiars is something unique to Fuyuki itself.
The preparations and arrangements were all handled by the Association, and they are more or less in charge of running the ritual. But, since it's a battle for the “Holy Grail” the Church refused to just sit idly by.
“It matters not if it is real or fake. It is our duty to manage the Holy Grail.”
With that, they dispatched a supervisor to Fuyuki, scheming to snatch away the Holy Grail from the magi should an opening present itself.
…Basically, the game software was developed by magi affiliated with the Association, but the rights to the hardware that runs the game belong to the Holy Church. Really, it's a pretty unreasonable setup.

Fate/side material: Fate Encyclopedia