Carnival of Time
The Carnival of Time[1][2][3] is an event that takes place in Clock Town annually, as mentioned in Majora's Mask. People come from all over Termina to celebrate the carnival and pray for a good harvest in the year to come. While it is never explicitly stated in-game that the carnival is also a "new year's" celebration, it is implied as such. The Carnival of Time takes place on the third and final day during Link's journey in Termina.
Customs
While in the past the tradition was to wear masks bearing the images of the four gods, it has become custom over the years for everyone to come wearing a mask that they have made themselves. The people of Termina wait anxiously for midnight of that day, as at that time the Clock Tower's entrance will open, and the tower itself "falls over", causing the clock face to be level with the ground. This allows people to go into the entrance and stand on the clock face as they make their prayers and sing ceremonial songs.
There is also a legend that states that if a couple unites on the day of the carnival itself (signified in Clock Town by the fusing of the couple's homemade ceremonial masks), then good luck will follow them.
According to Anju’s Grandmother
Anju's Grandmother can be found in a room on the ground floor of the Stock Pot Inn. If Link speaks to her whilst wearing the All-Night Mask, he can listen to either of two stories. One of those stories is entitled as "Carnival of Time", and is where most known information on the carnival comes from. Select that option and with the aid of pictures, Anju’s grandmother will tell Link the following story:
"Each year, the season of harmony begins when the sun and moon are in alignment. Paying homage to the way that both nature and time are tirelessly in the process of progressing... The Carnival of Time is when the peoples of the four worlds celebrate that harmony and request fruitfulness for the year.
For ages, people have worn masks resembling the giants who are the gods of the four worlds.
Now, it has become a custom for each person to bring a handmade mask to The Carnival of Time.
It is said that if a couple united on the day of the festival and dedicated a mask as a sign of their union, it would bring luck. The centerpiece of the carnival is the Clock Tower, and on the eve of all the festivities, the doors to its roof are opened... From atop the Clock Tower roof, a ceremony to call the gods is held and an ancient song is sung.
All of these festivities for the Carnival of Time are held so that we may ask the gods for a rich harvest in the year to come!"