Louise Belcher wears bunny ears as a signature accessory, a completion to her as a character and to hide whatever is underneath the hat, which is truly terrifying as translated by the looks of Tina and Gene once the hat was removed. The bunny ears define the character Louise Belcher but are also a gimmick used by the writers to make viewers ask, "Why?" as displayed in the season three episode, "Ear-sy Rider."
The season three opening reveals how much of a part of Louise the hat is and the monster that the hat has been hiding. During the entire episode, the viewer never gets to see Louise without her bunny ear hat, which makes her even more mysterious and intriguing.