The Room Key is a quest item in Majora's Mask. It one of the stepping stones for the completion of the Anju and Kafei quest. The key is for the Knife Chamber, which actually contains a chest with a Silver Rupee in it.
Obtaining the Room Key
On the First Day, if Link talks to Anju in the Stock Pot Inn at 2:00 PM or after. He will find that a room called the Knife Chamber has been booked by a person of the same name, so Anju will mistakenly think that it is Link that booked the room. At 3:45 PM, Link can witness Link the Goron coming in and becoming confused when he finds out that he has already checked in.
After acquiring the Room Key, Link must talk to Anju while wearing Kafei's Mask. She will tell him to meet her in the kitchen later that night, which can only be accessed once Link has full access to the Stock Pot Inn at all times during the day. This is only the beginning of the sidequest, which will eventually yield the Couple's Mask as the ultimate reward.