In Animal Crossing: New Leaf-Welcome Amiibo, the Katrina hats are the Celebration Hat and Tingle Hood. When players wear these two hats, the highest level of in-game opportunities are unlocked for the player, each day.
The Katrina hats are equal to the Daily Lucky Item. If a player is wearing a Katrina hat, and has the Meow task of finding the Daily Lucky Item, the task will be automatically stamped.
The Katrina hats work for all 24 different human programs. There are 12 Blue TPC card programs and 12 Pink TPC card programs.
In Japan, when people turn 60 years old, they have a special birthday party and wear a traditional outfit that includes a round red cap with pleats. The word for the special birthday is "kanreki" and it means the person is entering their second childhood. It is possible that Nintendo chose this design to show that very wise, but young at heart, players will use the Celebration Hat to enhance their game.
In the Legend of Zelda universe, Tingle is a middle-aged superfan of Link. Tingle dresses in a cosplay outfit that resembles Link's clothing. There are many LOZ references in the Animal Crossing games. It is possible that Nintendo chose this design to show that only very dedicated players of Animal Crossing: New Leaf-Welcome Amiibo would discover how wearing the Tingle Hood enhances their game.
How to get the hats:
When the Fortune Shop opens, and the player visits on a day that their TPC color and Astrological sign has been issued a Bad Luck program for the day, Katrina will offer them a Celebration Hat or Tingle Hood for 10,000 bells.
The two Katrina hats give all TPC card color and Astrological signs the highest level of gameplay possible, each day. The Katrina hats are the equal of wearing the Daily Lucky Item that Katrina or the Lovely Phone report for unlocking the highest level of gameplay experiences, each day.
The two Katrina hats are re-orderable at Nook stores and much lower in price than when they are initially purchased.
Note to other contributors: I have many pictures for this entry, but I don't know how to upload them :(