From Nookipedia, the Animal Crossing wiki
Keeping to the idea of Easter, the Bunny Day event revolves around an Easter Egg Hunting competition. 30 Easter eggs are hidden around the town, which can be opened to reveal either candy (18) or a Bunny token (12). Zipper will exchange one Bunny foil per item of furniture from the Egg Series. The villagers around town will not get involved in the events, but will talk about Zipper and finding mysterious eggs buried around the town. Each character gets his or her own set of eggs.
In New Leaf
In New Leaf, Zipper. T will ask players to find eggs of all kinds. There are 6 kinds of eggs.
If a player brings all 6 eggs to him, the player will obtain an egg basket. Players will no longer be able to give Zipper eggs. The player has to eat the eggs to get either candy, a prize ticket, or a grand prize ticket. He will accept prize tickets in return for items of the egg series. If any players get the grand prize ticket, they can exchange the grand prize ticket in return for a pic of Zipper. Prize tickets and grand prize tickets cannot be sold; however, candy can be sold for 100 Bells each.
Some people have recorded that if all rocks which contain stone eggs are not all destroyed by the end of the day, then the rocks will turn into regular unbreakable rocks, however, this is uncommon. Solutions, such as time-travelling to the day after the event, opening the game, and exiting without saving, have been mentioned.
The Egg Series
Zipper. T will give players one of the following items from the Egg Series each time they give him a Bunny Token:
Zipper will exchange prize tickets for Egg Series furniture, the Egg Series in Animal Crossing: New Leaf is slightly different from the Egg Series in Animal Crossing: Let's go to the City/Animal Crossing: City Folk, as now the egg TV can be obtained randomly from Zipper after giving him a winning ticket and if the player finds a grand-prize ticket they can obtain a pic of Zipper.