This series is a zany school comedy based on a 4-panel manga. It involves a lot of slapstick and physical humor, as well as incorporating the bizarre into everyday life, sort of like Cromartie High School, but with female characters who are a bit more aesthetically pleasing. It could also be said to be similar to Clannad if Clannad did a mood 180 and became a comedy instead of a tear-jerker. Because in both, you have cute high school girls with small, personal problems. But the anime Azumanga Daioh probably most resembles is Lucky Star. However, in some ways, it's better than Lucky Star, because the girls are less annoyingly cutesy and the feel is overall more real and less saccharine.
The series title has no particular significance to the story. "Azumanga" is a portmanteau of the author's name "Azuma" and "manga", while "Daioh" comes from the magazine in which it was originally published, Dengeki Daioh. In the anime, "daioh" is mentioned during the next episode previews, used in context with the meaning "great king".
— Wikipedia, "Azumanga Daioh"
Azumanga Daioh's comedy is largely character-based. Chiyo, a girl with orange pigtails, is a genius little girl who's moved up to high school by skipping grades. Sakaki is the athlete of the group, but she has a problem with cats not liking her. Osaka (not her real name, she's called that because she's from Osaka the city) is dumb, because apparently all people from Osaka are dumb. And so on.
As Wikipedia says, "It is generally realistic in tone, marked by occasional bursts of surrealism and absurdity, such as Osaka imagining Chiyo's ponytails being "unscrewed" from her head and an episode featuring the characters' New Year's dreams." Mostly, the show deals with things like studying, tests, grades, cultural festivals, extracurriculars, field trips, and the drama of dealing with teachers who can get just as crazy as some of the students. It's kind of like Sayonara Zetsubou Sensei, on happy pills.
Manga by Kiyohiko Azuma
Comedy, Slice of Life
Anime Film, Original Net Animation
I like this series because like I said, it's less sentimental than similar shows. It doesn't try to score moe points, it just makes its girl characters seem like real people, not like instruments being used to evoke emotions in the audience. These girls aren't the fragile little birds you see in other slice of life schoolgirl shows. They're bold, wild, and loud, unafraid to let their individuality show, and that's very refreshing.
While there are a lot of anime set in high school, many of them focus on something supernatural happening outside of school itself. So this is a show that actually focuses on school, and it feels very real, because it tackles challenges high school students actually face in the real world, in its own wacky kind of style. That way, the humor will best resonate with either high school students or people with vivid, funny memories of their own from high school. As for me, I don't like it all that much to be honest, but that's just because I'm no longer a high school student myself. But if you don't like magic and fantasy in anime, and want something silly, but still ultimately connected to real-life experiences, this is a good show for you. It also doesn't sexualize the high school students (other than joking about how one male teacher lusts after them), like many anime do. It's about real girls doing real things, getting into some hilarious situations.