The universe of Extra shares the events of the Fate/stay night universe until a "certain major incident" in the 1970s that caused the world's mana to start drying up causes it to split off into its own separate universe. As of the 2030s, the world's mana was completely gone.
The world is set in a school called Tsukumihara Academy, a fictional place existing with an artificial environment called the Moon Cell. There, the Moon Cell orchestrates a replication of the Holy Grail War using a system called Serial Phantasm or SE.RA.PH, which handles the summoning of Servants.
Servant data is taken from the Moon Cell Automaton, a spiritual computer system built on the lunar surface by a pre-human civilization and discovered by humans in the year 2032. The Automaton has monitored and recorded all occurrences on the Earth (including the activities of human heroes) since time immemorial. In this sense, it is similar to the Throne of Heroes. Unlike the Fate/Stay Night counterpart, all involved are either human personalities that function as NPCs, or hackers, resulting in what Rin herself called a "fair system," as it does not involve innocents. In addition, Servants are to convey the will of the Moon Cell above their own needs.
Each of the 128 participants in the war must duel the other Masters in a place called the Arena, where failure results in deletion from the digital world and death in the other. When only one remains, the "Holy Grail" shall grant the victor's wish.
Power of the Verse
Most of the characters of note are Massively Hypersonic with City to Mountain level attack potency; though, much of it is power-scaling from feats in Fate/stay night.
However, most of its power comes from the top tiers that appear in CCC. Causality Manipulation, Mind Manipulation, Soul Manipulation, and existence erasure are some of the hax that they have, all backed up with Massively FTL+ travel speed.