This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
New Eden was an Earth colony founded on the planet Terralysium in 2053. It was located in a forested area near a waterfall, south of at least some of the other settlements on the planet. It was sometimes virtually deserted as its inhabitants were active in the surrounding fields.
The founders of the town were Humans called the "First Saved", who were seeking shelter in their church from nuclear destruction in 2053 during Earth's World War III. The entire building was transported to Terralysium by Gabrielle Burnham using the Red Angel suit, causing the rescued to believe they were saved by extraterrestrial angels. (DIS: "New Eden", "Perpetual Infinity")
Their descendants were a very religious people, that taught about the angels at their church, which combined multiple Earth religions. They falsely believed that the colonies of their world were the only survivors of Humanity, and that Earth was destroyed in the 2050s.
The crew of the USS Discovery located this colony when they investigated a red burst. Since they were a pre-warp culture, the Prime Directive wouldn't allow the landing party to reveal their true origins to the settlers of the planet. Still, while they were there, the Discovery was able to stop radiation from the planetary rings from causing an extinction-level event.
Despite the Prime Directive, Captain Christopher Pike decided to reveal his true origins to one New Edenite named Jacob, as it was important that he learned more about the "angels" and their connection to the red bursts. (DIS: "New Eden")