The seasons are an interesting concept because they do not represent the same things for everybody around the world. Obviously, seasons are inverted in the northern and southern hemispheres, and tropical countries have no real seasons beyond "dry" and "wet".
In temperate areas, humans everywhere on the globe have divided the yearly cycle into 4 seasons, and this since ancient times. Yet, it could be argued that there are actually more than 4 seasons, if we observe carefully the evolution of nature, and take other factors into account, like rain, humidity or daylight. For instance, some countries have a rainy season within one of the four seasons. It is the case in Japan, where about 6 weeks of the 5-month long summer is the "tsuyu" or "rainy season". Temperature-wise, it could be said that subtropical regions (e.g. Florida, or most of Japan) have a high-summer (very hot and humid) and low-summer (less hot, but hot enough to be in tshirt).
The North of Europe has a particularity than no other densely inhabited regions of the world have, thanks to its high latitude : major changes in daylight between summer and winter. Indeed, if you look at a world map, New York or Beijing, on the north of their respective country, are at the same latitude as the south of Spain or Italy. Even Montreal in Canada is at the latitude of central France or southern Germany. Europe is a much warmer continent than Asia or North America because of the Gulf Stream, a warm current from central America that blows warm air on the British Isles and the rest of Europe (hence Britain's notoriously cloudy weather).
Let me describe the weather in the region of Europe I know the best : the Benelux, Southern England and Northern France.
Early Spring (late March to early May)
Cherry trees, apple trees and magnolias are budding, then blossoming. The snow-drops, then daffodils, then tulips bloom. Birds start making their nests. The weather warms up little by little, but rain is frequent and the weather very changy, with occasional frost at night and possibilities of hailstones in the late afternoon. Days are starting to become longer.
Late Spring (Early May to mid-June)
Leaves start growing on trees, radically changing the bleak winter landscape into cheerful green scenery. Bushes ad shrubs blossom in yellow and pink colours. Flowers are becoming more common on balconies, in gardens and parks. Bird eggs hatch (and cats catch careless youngsters). Cows, sheep and horses are back in the fields. The weather stays unstable, with an alternation of cool and warm days, rainy and sunny weather. The sun rises early and sets around 8 or 9pm.
Summer (mid-June to mid-September)
Everything is green and full of flowers. Some fruits (e.g. cherries) become ripe. Cereals are growing well in fields. Days are warm, and sometimes hot. Daylight reaches its peak in late June, with sunset around 10:30pm (9:30pm in England due to the time difference), then days get increasingly shorter, with sun setting around 8pm in mid-September.
Early Autumn (mid-September to mid-October)
It is the fruit season par excellence, with apples, pears, plums, grapes, and all kind of nuts (hazelnuts, walnuts, chestnuts...) filling the trees. It is also the harvesting season for cereals. The weather is still fairly warm and days aren't so short (sun set around 7pm in mid-October). Leaves are starting to change colour and fall.
Late Autumn (mid-October to early December)
Leaves on tree are all yellow, red or brown, then fall completely, leaving all trees bare (except conniferous, of course). Forest, parks and tree-lined roads are filled with dead leaves. Days are becoming much shorter and cooler. It is time to turn the heating on again, wear warmer clothes, and turn on the lights at home when cooking dinner. The weather is particularily foul and rainy.
Winter (early December to late March)
Temperatures drop, with frost common at night, and some days of snow (always less because of global warming). Sun rises as late as 8:30am and sets around 4:30pm late in December. On cloudy days (which are common), lights are often turned on all day long in homes, schools and offices from mid-December to mid-January. January and February are typically the coldest months. It rains a lot, with floods hitting some regions every few years.
