Hyperia is name given to this world by Aselia in Eien no Aselia (Spirit of the Eternity Swords 1). This is the world where the Eien no Aselia protangonist Etranger Yuuto and his friends (Kaori, Kyouko, Kouin, Shun) and possibly previous Etrangers came from. Originally, Yuuto is at a loss for the name of his world as he notes that "Earth is just a planet" and that there were other planets in this universe as well. Aselia suggests Hyperia over dinner, thinking that Yuuto's world is the same as the one that "is above [Phantasmagoria]... celestial world of the shining moon, beyond the vast sea and the Dragon's Claw Marks... where people [not spirits] are said to be taken when they die."
As Yuuto didn't have a name for his world, this one just stuck.
"Copy World" is the name this world is given when visited by Nozomu and gang in Seinarukana (Spirit of Eternity Swords 2). [Identity of this world is surmised from the presence of Kaori, Kotori, and Tokimi; existence of multiple Kaoris or Kotoris or Tokimis not ruled out]. This world is one of the branch worlds from the Time Tree.
Not to be confused with Earth, Original World (according to Nozomu and gang).