From Bulbapedia, the community-driven Pokémon encyclopedia.
Princess Day (Japanese: ひなまつり Doll Festival) is a holiday celebrated throughout the Pokémon world. It is the equivalent of the real-world Japanese holiday Hinamatsuri (means Doll Festival, but sometimes referred to as Girls' Day).
Like in the real world, it is traditional for girls to display a set of ornamental dolls representing the Emperor's Court. It is commemorated by various events, girls' only Pokémon tournaments, and other activities and sales, which are for girls only.
Princess Day was shown in the anime episode Princess vs. Princess. Misty and Jessie reminisced about past Princess Days, while competing for a prized Pokémon doll collection.
Princess Day Festival
The Princess Day Festival is a competition consisting of Pokémon battles. Each Trainer must use exactly four Pokémon to battle. The battles are split into two separate divisions, and the winner of each division proceeds to the finals. Each Trainer entering the festival is required to be female. Every competitor wears a formal traditional Japanese outfit, with a Kimono and usually a fan. Before the actual competition, the contestants all stand in a row on stage as people gather to watch. The only confirmed winner of the Festival is Misty. The prizes she won from the festival were a brand new set of Pokémon Dolls, and a chance to meet superstar Fiorello Cappucino, who was also an announcer of the festival.