Corneria is yet another stage that debuted in Melee. And like Brinstar it seems based off of a Smash 64 stage, this one being Sector Z. Unlike the other two returning stages from Melee to the 3DS version, this one doesn't seem to have aged as well graphically. It also still has the Star Fox codecs so that's something.
The stage takes place on the Great Fox as it flies through Corneria. Ocasionally, an Arwing will fly by, allowing you to climb on it and die when it flies away or get shot by its lazers. Your choice.