The title of the show is essentially meaningless. The comic strip on which the show is based was written by Azuma Kiyohiko, and "Azumanga" is an amalgalm of his name and "manga", the Japanese word for comic books. "Daioh" comes from "Dengeki Daioh" ("Great Electric Shock King"), the monthly Japanese comic anthology in which the comics originally ran.
The show was originally broadcast in four-minute segments every weekday on the TV Tokyo satellite channel. Each week's daily segments were reshown as a single 24-minute episode on Saturdays. The Saturday episodes also featured additional footage not screened in the daily segments, including longer opening and closing credits, a preview of the next week's episodes and in some cases a short prologue or epilogue, which accounts for the longer running time than that of the individual segments.
According to interview done for an art book of the series, the director made a request for the opening song to not have any tone changes or climatic phrases, hence leading to the extremely catchy piece "Soramimi Cake"
Episode 19 "One Spring Night" is a "filler" episode made up of jokes and scenes that were not in the original manga.