Apparently there were some references to this in ArM4, but it seems to be gone from 5th edition. Anyone who can tell me what this apparent calendar approximately means?
Its an astrological calendar. You know the song.. "its the dawning of the age of aquarius" 
The idea is based on the Precession of the Equinoxes, the fact that due to the orientation of the Earth's axis slowly changes. This means that the Equinoxes seem to move relative to the fixed stars. An Astrological Age is about 2160 years (though there's another way of measuring that causes each age to vary in length).
A basic problem is that Ars Magica's time frame is quite clearly in the Age of Pisces, not the Age of Aries (which ended some time between 100 BCE and 500 CE depending on your choice of measurements).
It sounds cool and all, but I suspect it was dropped in 5e because 1) hardly anyone knows what it means and 2) its EXTREMELY fuzzy.
Ah, ok, thanks alot for the answer. That thing had me quite puzzled 
Well, hardly anyoe knows what it means because the books never explicityly told anyone. Frankly, I find the idea that the Order uses a different calendar, and one which links in to the astrological influences on their magic, both proper and flavourful. I can see how giving every date twice in the books might get wearing, but it was a nice touch.
I like the flavour, but I find the justification for the bad astrology (in the old 'Mysteries' book?) a bit weak. On the other hand, magi are quite traditional and if it was good enough for the Founders then maybe it is good enough for you?