Yotsuba&! is a slice-of-life comedy set in a small Japanese town and written by Kiyohiko Azuma. It's the story of Yotsuba Koiwai, a quirky five-year-old, and her life after she and her adoptive father move to a new town. The story focuses on Yotsuba, her father and his friends, and the neighboring family, and deals with many of the events that occur during in daily life in Japan, like shopping, school festivals, summer homework, and typhoons. The humor of the series comes primarily from Yotsuba's lack of knowledge about things a typical five-year-old would know, and the resulting way that she misunderstands a lot of what goes on around her. (If I'm making this sound too dry, trust me, it's not; this series is hilarious. My favorite parts are when Yotsuba and Yanda--a friend of her father's who became Yotsuba's enemy when he ate her ice cream--get into childish arguments with each other.)
Yotsuba&! is a change from Azuma's previously translated series, Azumanga Daioh: Yotsuba&! is drawn in a standard manga page format, while Azumanga Daioh was a series of four-panel comics (kind of like the comic strips in newspaper, except in Japan comics are printed and read up-to-down rather than left-to-right).
Yotsuba&! is published by two different translation companies: ADV Manga published the first five volumes, and then sold the title to Yen Press, which reprinted those five and has continued with the following volumes. This means that if you go from reading ADV Manga's translations to reading Yen Press's, you'll find some differences: one of the character's names is spelled differently (Fuka in ADV's, Fuuka in Yen Press's), and a few of the jokes are different. This reflects the two companies' different appraches to translation: ADV aims to make the translation as accessable as possible for the widest range of readers, while Yen Press tends to focus a little more on readers who already have a familiarity with manga and Japanese customs and spelling (the difference between Fuka and Fuuka is that romaji--the Japanese alphabet--has many double vowels, while in English that's pretty rare). But Yen Press includes notes to avoid being too obscure.
(I mention all this because at Mooresville Public Library, the first five copies of Yotsuba&! are by ADV, so don't be surprised when you spot the changes in volume 6!)