Eridanus II is probably a play on Eta Eridani a real life star that translates as "Hatching Place" or "Breeding Place")
The planet is an orange gas giant in the Eridanus Star System which including Eridanus II has a total of 12 planets.
A UNSC colony world, little has been revealed about this planet, but it is the location of the Luxor Spaceport and Elysium City, where John-117 grew up until he was abducted and sent into the Spartan program in 2514. He later returned there in 2525 with the other Spartans aboard the frigate UNSC Pioneer to board the cargo freighter Laden and travel to a rebel base, Eridanus Secundus. They likely boarded this vessel at the spaceport.
The Spartans later returned to the system in 2552 aboard the captured Covenant flagship Ascendant Justice, returning to the Rebel base.
How there could be a colony on a world without a breathable atmosphere, or even surface, is unknown, though it is possible that the colony consists of floating domed cities or towns in the atmosphere of Eridanus II. Dr. Halsey mentions "climate-controlled weather" on page 22 of The Fall of Reach, suggesting domed environments, a neccesity on a world without a breathable atmosphere.
The colony of the planet was destroyed by the Covenant in 2530.