Discordianism is a principle concerned with the nature of disorder vs. order. Among other things, it purposefully contradicts itself in a number of ways. One of its benefits is a very regular calendar: All years have the same number of weeks and a new year always starts on the beginning of a week. However, the Principia Discordia is somewhat vague over how leap days should be applied - therefor, the widget can display the current date aligned either to the Julian or the Gregorian calendar.
You can read more about the Discordian calendar on Wikipedia: http://en.wikipedia.org/wiki/Discordian_calendar