The Couple's Mask is one of the twenty four Masks from Majora's Mask.
When it is worn, Link can talk to the people arguing in Mayor Dotour's office of the Mayor's Residence to make them stop and receive a Piece of Heart. Other than this event, it has no other use.
Obtaining the Couple's Mask
Complete the Anju and Kafei Side Quest.
Model of the Couple's Mask
Link receiving the Couple's Mask