Michaelmas was a medieval holiday, celebrated on September 29.
In 995, Constantine set the date of his intended wedding with Princess Katharine on Michaelmas. However, Katharine, along with the Magus, Tom, Mary, Finella and the eggs, fled his castle for Avalon the night before the wedding on Michaelmas Eve. ("Avalon" Part One)
Many other important events in the Gargoyles Universe took place on Michaelmas. Among these were the coronations of King Arthur in 500 and Macbeth in 1040, and Hakon's initial attack on Castle Wyvern in 994. ("Rock & Roll")  Michaelmas Eve (September 28) was the date of Vinnie's birth in 1963, Demona's recovery of the Praying Gargoyle from Notre Dame and murder of Charles Canmore in 1980, and Demona's summoning Puck in 1995. ("Awakening: Part One", "Hunter's Moon" Part Three, "The Mirror") 
Real World Background
Michaelmas was dedicated to the Archangel Michael, after whom it was named. During the Middle Ages, it marked the beginning of the fiscal year, and is still one of the four quarter days (when rents are due) in England (the other three being Annunciation Day - March 25, Midsummer's Day, and Christmas). It was customary to eat goose on that day.
Greg Weisman's birthday is on September 28, which is often why both Michaelmas and Michaelmas Eve play such a notable role in the show's chronology. The events from the "Awakening: Part One" flashback, however, were tied to the holiday so it could coincide with the World Premiere of Gargoyles at the multiplex on Pleasure Island at Walt DisneyWorld in Orlando, Florida (September 29, 1994). 
- Michaelmas at Wikipedia, the Free Encyclopedia