The truth is, I would say Japan has more than just four seasons, because of the month of tsuyu, monsoon rains, in June. Historically more than 30 seasons were recognized in the Japanese calendar, and they regulated everything from agriculture to religious festivals to what color/pattern kimono you could wear.
Even today, Japanese people love their seasons, which are quite regular, predictable, and generally show up on time every year. The Japanese make a bigger deal about each season's characteristics than most Americans do, so I can understand why the above sentence makes it into nearly every travel brochure. For city-bound Japanese, the change of seasons is most noticeable in the decor of supermarkets and department stores and the foods available therein. In the countryside there are more festivals and agricultural events that mark the change of seasons. As an exchange student, I remember being glad I chose the year-abroad option as opposed to a semester abroad, so I could enjoy a year of Japanese seasons. Now coming up on my 4th year in Japan, I've experienced each season a couple times, and there are lovely things to enjoy about each one. Here are a few:
I will start with spring since it is spring now! Spring is flower season. The most famous are the plum blossoms which bloom earliest at the beginning of March. They bring to mind ancient Chinese poetry and influence in Japanese culture. Then comes the queen of Japanese flowers, the sakura or cherry blossoms in the beginning of April. In Kyoto in particular, cherry trees have been planted everywhere, so the city blossoms with the light pink sprays. It always seems to coincide with cherry blossoms that the sky also changes from pale wintery hues to the deep blue that heralds summer. The sun's light is stronger and makes the cherry trees seem to glow with their own brilliant light.
At the end of April, wisteria (藤）is in bloom. I've discovered a few parks here and there that grow it on big trellises for viewing pleasure at this time of the month, I think I like them better than sakura if possible.
At the beginning of May, there is a 4-day string of national holidays "Golden Week" so everyone tries to go out and travel! You have to book tickets/hotels well in advance if you travel during this season. In rural Japan (not so much in Kansai?) there is the traditional kite-flying festival Children's Day, where families with male children hang out huge carp-shaped kites. May is my favorite month in Japan. No bugs yet, not too hot, not chilly, and late spring green is everywhere. I especially like going to see green momiji (maple) leaves in May.
After tsuyu ends (it will say on the news the official end of the season as calculated by meterologists) the temperature jumps and real summer starts. Cicadas appear in hordes and make every tree vibrate with their cacophony. In summer there are two great festivals to enjoy in Kyoto, Gion Festival (extremely crowded but good for festival food and people-watching) and Tanabata (held a bit later than most of Japan's tanabata holiday, celebrated with beautiful illuminations "light ups" along Kamogawa and Horikawa rivers). In summer the best thing to do is stay hydrated and go out only in the evenings, again making these nighttime festivals a lot of fun!
October boasts blessed relief from the hot summer with cool nights and mornings, but with bright days making it a great month for finally leaving the house (and AC) and venturing out to sight-see.
The momiji at the end of November are the last bit of natural color you can see until the plum blossoms next spring, and I find them very romantic. The best places to see them get extremely crowded but hit me up for some secret lovely spots^^
Winter in Japan is COLD not because temperatures are so extremely low (actually it's about the same as my hometown in the Seattle area) but because Japanese houses are made without much insulation or central heating. The cold air is unstoppable and portable heaters can only heat one room at a time, so you have to freeze to take a shower or bundle up to use your kitchen. I get so grumpy and tired of winter in Japan, the days and mountains are grey, pale, and colorless and I can never get warm. Winter is a time for hunkering down in kotatsu (a low table with a heating element underneath and a thick quilt down the sides), onsen (natural mineral baths), and eating nabe--hot-pot soups. Those who like winter sports will find easy access to the mountains and popular ski spots, but it's something I've yet to try.
The most important Japanese holiday on the calendar, New Year's, is very fun if you have access to a Japanese family: think 3 days or so of eating snacks and lazing around, watching end-of-the-year TV specials, and counting down to midnight with a...4-hour televised singing contest? Yes and then getting up very early to either see the first sunrise of the year or visit a shrine, 初詣、for good luck in the next year. Many Japanese families send New Year's greeting postcards or have their kids try making mochi (pounded rice). If you don't have family to spend it with, New Year's in Japan can be even lonelier than Christmas, since your Japanese friends will scatter to spend the holiday with their families and many shops and services are closed. You might get stuck in a bar watching the Times Square ball drop with other lonely foreigners.
So there are the major events/seasonal activities one can enjoy throughout a year in Japan, at least from my limited experience. Winter is probably my least favorite, followed by summer. Spring and fall are heavenly! I'm looking forward to some springtime adventures, as health and work schedule allows!