What is a Compact Calendar?
It's a means of condensing any one of its forms -- annual / centurial /
/ multi-centurial (Julian + Gregorian) -- by avoiding the over-repititious information on standard presentations of our calendar. 
The 2001 calendar you are familiar with, is thus reduced to a single presentation for a whole year instead of the usual twelve. 
There is one version covering a century,  and another calendar which covers 25 centuries!
A by-product of adopting these compact calendars worldwide would be the ginormous number of forests which could be saved by the great reduction in the need for paper.  Current calendar manufacturers have been the greatest detractors of this invention.

Who invented these Calendars?
Ted Clarke in Cornwall.

What is different about the Compact Calendar?
The whole calendar for a year, or a century and even a number of centuries can be placed on one page. This saves the need for having a new sheet for every day or month as most calendars do.

The structure of the Compact Calendar
The design provided by Ted Clarke has only been possible by using his intimate knowledge of the structure of the Gregorian and Julian Calendars combined with an exceptional ability in solving mathematical puzzles.
Variations he has provided enable one for example, to easily predict the day on which Easter will fall in any given year. 

The functions of the Compact Calendars 
They are especially useful for historical research and genealogical purposes. Authors of historical novels will appreciate their convenience, with no need to refer to a "book" of calendars.
Not to mention the pure fascination of their novelty.

More references to Compact Calendars can be found in Ted Clarke's new book "HOW THICK IS A SHADOW?"