This is the six day postponement before the main event of the Moon’s Holy Grail War.
It’s a time to train and prepare oneself for battle, to find out about your opponents, and to deepen your relationship with your Servant.
The Masters who make no effort to improve themselves during this six day period are met with death, which comes in the form of “Omission” (from the main event).
The Moratorium is based on Erickson’s proposal, “After a human reaches adulthood, this is the postponement of carrying out their social responsibilities and duties. Or otherwise, the state of mind where one tries to remain indefinitely in the postponement period.”
While it may seem cruel, these six days are a “rite of passage [to adulthood]” and constitute Moon Cell’s idea of fairness to the competitors.

On the far side of the Moon a certain young girl sneers:
“You Masters have no need for a Moratorium.
Live alone,
Worry alone,
Destroy yourself alone, please.”
Such an end will meet the people who close themselves up in their own little world and deem others to be unnecessary.

Translator’s Notes
  1. ^ Also known as “Preparation Period.”
Fate/EXTRA Material: Encyclopedia of Fate/EXTRA