From Halopedia, the Halo wiki
"Eden" was a term used to describe a beautiful garden the Librarian made on Earth, not far from the Portal to the Ark. The Librarian described the garden in her final message to her husband, the IsoDidact, before she ceased all communications. The message was recorded in a terminal found on Installation 00.
It is important to note that "Eden" would not have been the actual name used by the Librarian. The Librarian's transmissions were discovered using translation software so advanced that it incorporates idioms from the reader's own experience. Thus words such as "Eden", "fairy tale," or "Maginot Line" became the default usage in Forerunner terminals and transmissions when read by humans. Since there is no direct translation for the original Forerunner words, the software utilizes the closest human equivalents (shown in brackets in the terminals); in this case, "Eden" idiomatically refers to the biblical Garden of Eden, often used as a symbol for an earthly paradise.
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