They are the "four seasons," shiki 四季.
- natsu 夏
- haru 春
- fuyu 冬
- aki 秋
(don't mistake natsu 夏 with nanatsu 七つ, which means "seven")
Unless you're playing bukujou monogatari 牧場物語 (Harvest Moon) or you're in an actual "farm," bokujou 牧場, however, most of these seasons don't really matter.
I mean, natsu 夏 and fuyu 冬? It gets atsui 暑い and samui 寒い. But haru 春 and aki 秋? Does anything even change in those seasons? If you aren't dealing with plants or animals you probably can't even tell which comes after winter and which comes after summer!
What is Natsuyasumi
So the import seasons are natsu and fuyu, and about natsu we have the common Japanese word natsuyasumi 夏休み, which often shows up in school anime and manga. The word means very literally "summer rest" and less literally "summer vacation." It's the summer break between school semesters.
The verb yasumu 休む means to "rest," together with natsu 夏, which is "summer," is how you get that word. It's not complicated at all.
There is, indeed, a word for fuyuyasumi 冬休み, which would be "winter vacation." But let's be honest: who cares about winter vacation?
You can't go to the beach during winter vacation. It snows, you know? "Snow," yuki 雪? Yeah, winter is full of that. So there is no point in having episodes about winter vacation as the characters can't go to the beach and there will be no fanservice of girls in bikini splashing water around.
Like I said, there are anime character names with the words natsu, haru, fuyu and aki. This happens because, in Japan, Japanese names are often written with kanji and these kanji be literally anything, including, of course, the kanji for the four seasons.
This doesn't really mean anything though. If a character is called natsu, the name natsu means nothing. I mean, it's the kanji for "summer" what the hell could it mean? Did the mother go "oh, my son looks like a summer, so I'll call him summer?" Maybe it was hot the day he was born? Maybe the father liked the shape of the kanji? The name means nothing!
Anyway, here are some examples of what I'm talking about:
Names with Natsu 夏
- Katou Natsumi 加藤 奈津実 (♀)
- Shinohara Natsuki 篠原 夏希 (♀)
From Summer Wars
- Sagan Natsuo 目奈 津生 (♂)
Names with Aki 秋
- Sorachi Hideaki 空知 英秋 (♂)
gorillamangaka 漫画家 from Gintama 銀魂
- Furukawa Akio 古河 秋生 (♂)
- Senomiya Akiho 瀬乃宮 あき穂 (♀)
- Kogami Akira 小神 あきら (♀)
From Lucky☆Star らき☆すた
Names with Fuyu 冬
- Irisu Fuyumi 入須 冬実 (♀)
From Hyouka 氷菓
- Kudou Fuyuka 久遠 冬花 (♀)
From Inazuma Eleven
Names with Haru 春
- Suzumiya Haruhi 涼宮 ハルヒ (♀)
From Suzumiya Haruhi no Yuuutsu 涼宮ハルヒの憂鬱, (The Melancholy of Haruhi Suzumiya)
(in Japanese it's written with katakana, but in Chinese it would be haruhi 春日)
- Fujioka Haruhi 藤岡 ハルヒ (♀)
From Ouran Koukou Hosuto-bu 桜蘭高校ホスト部 (Ouran Highschool Host Club)
- Haruhara Haruko ハルハラ ハル子 (♀)