Tail Key

The Tail Key is one of several keys in Link's Awakening used to open a dungeon.

After Link sprinkles Magic Powder on the raccoon in the Mysterious Woods, he finally has access to a hidden chest on the next screen. The chest contains the Tail Key, which opens the first dungeon, Tail Cave.

Trivia
The Moldorm boss of the Tail Cave featured in Link's Awakening (as well as the one in A Link to the Past) is known as Degu Tail in Japanese; which explains the name of this item.