I've read nothing but rave reviews of this manga, full of such words as "irresistible," "heartwarming" and "outstanding." And for the life of me, I completely understand why. People like this good manga so much. We are so starved for a break from the endless psychic schoolboy angst stories that we'll lap up witty humor such as Yotsuba&! without question.
While working my way through volume 1 of Yotsuba&!, the words that came to my mind were "awesome," "cute" and "entertaining." As well as multiple praises and bits of laughter. The manga is about a small child that reacts to everything she encounters with spastic bewilderment. At the start of the book, she moves into a new home. Her new neighbors are a trio of girls who are prone to fits of hysterical sexiness at the slightest provocation. And so, we're treated to Yotsuba and friends engaging in such thrilling activities as ringing doorbells and going shopping, with lots of hysterical sexiness, and extremely funny "wacky" faces along the way. It's a very dynamic experience, and that experience happens to be one of light-hearted humor. You can imagine how that gets awesome very quickly.
As for the art, I believe Kiyohiko Azuma can draw fairly well, as evidenced by the charming titls page or cover illustration. He chooses to, as evidenced by everything else. Characters spend nearly all their time in "komickal" mode, which means their heads are rendered as featureless blobs with some minimalist doodle filling in for their faces, which adds to the lighthearted charm of the manga. And someone apparently has to pull the exact same cute "augh!" face at least once per page. Hilarious? More like extremely hilarious and rad. Our friends Detail and Finesse are also still in the building, leaving everything with a believable, simple, minimal look. This sort of art is usually glossed over with the euphemism "stylised," and it's high time someone appreciated it. The art looks like no effort whatsoever went into it, which is fine, since the purpose isn't realism anyway.
If you also happen to be a small child that is permanently high on life, or you derive some kind of understandable satisfaction from having your intelligence put to the test, I recommend you read Yotsuba&!. As for why it's so incredibly popular, I can understand that, and thinking about it actually rather comforts me.