Eden had two moons. While the planet's atmosphere was capable of supporting humanoid lifeforms, the planet was completely devoid of fauna. All the plant life, even the grass, was filled with acid that resulted in severe burns upon touch. The fruit on the trees was poisonous. This made the world virtually uninhabitable to humanoid life. (TOS: "The Way to Eden")
In 2269, the Tiburonian research engineer Doctor Sevrin began a quest to locate the mythical planet Eden, which he believed to be an idyllic, undiscovered planet. Gathering a group of loyal followers, Sevrin stole the space cruiser Aurora and embarked on his search. Sevrin and his followers were eventually located and apprehended by the crew of the USS Enterprise, although they were later able to take control of the ship.
Sevrin set the Enterprise on a course for Eden in Romulan space. Spock and Pavel Chekov had discovered the planet earlier by searching for an uncharted celestial body that corresponded with what Sevrin was looking for. They found the world by studying star charts and projecting the orbits of various planets. By mathematical processes, they were able to discern the location of this world by the effect it had on other known planets.
After the ship had crossed the Neutral Zone, the Enterprise arrived at the planet, to the surface of which Sevrin and his followers traveled in a shuttlecraft. Sevrin and the others were distressed to find, however, that the planet was uninhabitable to humanoid life. The party received severe burns on their bare feet, and Adam died from eating poisonous fruit. Sevrin himself also ate poisonous fruit and died to stay on Eden. After returning to the ship, Spock told Irina Galliulin, one of Sevrin's followers, not give up the search for Eden, including making it themselves. (TOS: "The Way to Eden")
In 2399, the location of Eden was labeled in a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This planet was in or near to territory claimed by the Romulan Free State. (PIC: "Maps and Legends")
According to Star Trek: Star Charts (p. 66, "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Eden orbited a G-class star.
The background of the remastered version appears to possibly be a modification of a photo of the floor of Yosemite Valley.
According to Star Trek Maps (p. 25), Eden was the only planet that orbited the moderate white star UFC 3676543. It was first discovered by shipwrecked survivors of the Earth-Romulan War, who passed on stories of its mythical beauty.