Talk of the seasons can be confusing because different people mean different things.

The most common system uses the astronomical basis of the equinoxes and solstices, so spring starts on March 21, summer June 21, autumn September 21, and winter December 21.

Meteorologically speaking though we use clean calendar months:

winter:     December, January, February

spring:     March, April, May

summer:     June, July, August

autumn:     September, October, November

We also talk about the "extended summer", which comprises the five months of May, June, July, August, September.

And according to the mediaeval church calendar, the seasons are summed up as: "Dat Clemens hiemem, dat Petrus ver Cathedratus, aesuat Urbanus et autumnnat Bartholomaeus". This means that winter lasts from the feast of St Clement (23 November) until February 21st; spring from St Peter's Day [which then I assume was February 22nd] until the feast of St Urban [presumably May 21st]; and summer from then until August 23rd.; and autumn began on the feast of St Bartholomew on August 24th.

In the UK there are no clear cut boundaries. The start of each season is a stop-start affair that often by most measures start and end outside the usual boundaries. Recently we have seen some lovely "spring days" in February and even January. In 2012-13 the coldest month of the "winter" was March. And occasionally the hottest and coldest days of the year fall outside summer and winter respectively. Most spectacularly, in 2023 the coldest day of the year fell occured in spring, and the hottest day of the year in autumn.

Philip Eden argues that spring begins when the growing season for most plants begins, which very roughly is when the average temperature is above 6ºC. That's March for most of England, but in Scotland we're looking at April.

Note that in the southern hemisphere the seasons are reversed.