The Lunar Wing is a key item introduced in Generation IV. In Diamond, Pearl, and Platinum, you need the Lunar Wing from Fullmoon Island to heal a boy in Canalave City. Once you get it from Cresselia, Cresselia flees and is found at random throughout Sinnoh.
Anime
Lunar Wing in the anime
The Lunar Wing are feathers of Cresselia. These feathers help keep the nightmares (that Darkrai creates) away from residents of Canalave City. A Lunar Wing looks like a feather that has a curl with an enchanted green (top-half of the feather). It has a yellowish end.
It makes an appearance in MS010: Pokémon - The Rise of Darkrai, where Dawn buys one for Ash after he wakes up from the nightmare/vision given to him by Darkrai's Dark Void, in case they met again.