K-ON! is inconsequential fluff. One might compare it to popcorn or cotton candy: a tasty treat, but if you're looking for a meal, it will leave you looking for something more substantial after it's done.
K-ON! follows the tried and true formula of cute girls doing cute things. Based on a 4-koma comic, the series is about several high school girls who form (technically join, but all the previous members graduated) a light music club and follows their activities. The music itself often takes a back seat to the antics of the girls, and audiophiles may find themselves somewhat disappointed if they go in expecting detailed attention to techniques or references to real life bands (there are a couple, but few and far between). There are two concerts in the thirteen episode series, but neither is as impressive as the one from the Live A Live episode of The Melancholy of Haruhi Suzumiya (one of Kyoto Animation's earlier shows), but still very enjoyable. The most common scene in the series features the main girls sitting in the club room snacking on tea and cakes while discussing various mundane events, particularly with the more dedicated girls trying to get the rest to practice.
The girls all have their own distinct personality. Yui, the main character, is the some clumsy and adorable airhead. She joined the club hoping to play an easy instrument like the castanets but ends up playing guitar because the club needed a guitarist. Ritsu is the energetic idiot of the show, drummer, and club president because she was the one who dragged everyone else into the club. Mio is Ritsu's long time friend, and the sensible, serious one of the group. She writes the groups songs, and plays the bass. She is also the most moe character, being the prettiest, easily embarrassed, and terrified of ghosts and yucky things. Mugi is the pianist. She comes from a wealthy family, and thus is a source of amusement by displaying the difference in wealth between rich people and normal people. She is also the provider of the tea and sweets that are regularly consumed at the club meetings.
There are a few regular minor characters, too. Ui is Yui's younger, but more mature and reliable sister. Yui has a friend named Nodoka who joins the student council, which means her role is essentially to let everyone know that Ritsu has forgotten something regarding paperwork for the club. Sawako is a music teacher who is recruited as the club adviser in one of the more memorable scenes of the series. Also, a late addition to the cast is Azusa, an underclassman who is much like a miniature version of Mio.
Character designs are generally cute, with the kind of big round faces typical of most Kyoto Animation works. Background art is consistently good, as is the animation, which should come as no surprise. When characters are shown playing their instruments, there is generally more attention to detail than seen in anime to the point where the sound properly matches the characters actions. The singing at the concert features the same style animation as Live A Live, where you can just about lip read the lyrics (if you know Japanese, of course).
The music used in the series can generally be described as light and fluffy, both the background music and the couple of songs the girls play at their concerts, with the exception of the closer, which rocks a little bit harder than rest. The voice acting fits well all around, with Yui being notable for regularly coming off as someone who isn't all there, fitting her character well.
I don't want to close saying this show is like Azumanga Daioh with a music club, but that's about the easiest comparison I can make, and not too far off a description.