|Courtesy of Mark A. Mandel|
A sense of order in a chaotic universe is comforting. The objective of a calendar is to bring order and where these things change, other things follow. The world doesn't always fit neatly into a numerical model - witness leap years as a hack to get around that. Of course if you change the rules, as Pope Gregory XIII did to try and keep Easter where it should be, there will be differences of opinion - and in RPGs, often that kind of philosophical difference leads to a fight.
This is easily transplanted into a game as long as consistency is applied. Perhaps a particular calendar day is favoured by one or more divine powers. Celestial events may be ordained to occur and certain numbers may hold arcane significance. The plot hooks that can be spawned from this are multifarious - want to foil an evil ritual? You need to be there on this date. This builds a sense of tradition and permanence as long as the events are observed in the game. There is little point having all this neat stuff if your players don't see it.