Salaries, rents and interest in England were payable on the four quarter days: Lady Day (Annunciation) (March 25), Midsummer Day (St. John the Baptist (June 24)), Michaelmas (September 29) and Christmas (December 25). Scotland had different quarter days: Candlemas (February 2), Whitsunday (May 15), Lammas (August 1), and Martinmas (November 11).

Lady Day is the feast of the Annunciation, nine months before Christmas. Under the Old Style calendar used in England until the mid-18th century, the new year began on Lady Day rather than January 1, so that started the cycle of quarter days.

Candlemas is the Feast of the Purification of the Virgin. It falls on the 40th day after Christmas; under Jewish law, a woman who had given birth to a son was supposed to undergo ritual purification on that day. See Leviticus Ch. 12.

I hadn't thought about the fact that Candlemas falls on the same date as the American Groundhog Day. Brewer's Dictionary of Phrase and Fable says that there was a Scots proverb that a dry, fair Candlemas meant winter was only half over, but a wet, foul Candlemas meant winter was already half over at Christmas. Brewer also notes a German proverb that the badger comes out of his hole on a snowy Candlemas but stays in if it is sunny. Somewhere between these two beliefs seems to be the origin of Groundhog Day.