King Pig's Castle is a limited time event in which the goal is to pass five levels with a single life.
When the event begins, you'll see an event button on the map screen. From the button you can enter the King Pig's Castle, a mini map that includes five levels. The goal is to complete all of those five levels without losing a life, in order to be able to open the treasure chest in the end. In case you fail one of the levels or you quit a level, your progress on the map is erased and you'll have to start over from the first level again.