There are four Quarter Days, as one would expect, which are Lady Day (25th March), Midsummer Day (24th June), Michaelmas (29th September) and Christmas (25th December).
Midsummer Day is not the same as the Summer Solstice, but is often confused (or conflated) with it.
The Quarter Days were the days on which rents, taxes etc. were to be paid.
The first of them (Lady Day) is still the day on which the UK Tax Year starts, albeit the date has moved to 6th April when such things moved eleven days at the change from the Julian to the Gregorian calendar.