K-On...well, there's this club. In Japan, they call it the "light music club"...here, it's the "pop music club". There's only four members...and one of them doesn't really get how to play music.
So that's the basics of it.
To be more in-depth, K-On is a manga about a group of girls who join a club to prevent its closure. But with only three members, they're unable to maintain their status. To make up for this, they rope in Yui Hirasawa. She's not the brightest bulb and a bit on the clumsy side, but they get her a guitar and off they go. The manga documents their activities together.
Before I read the manga, I had already watched the anime. The whole thing is very light-hearted and not that plot-focused. If you're going to understand K-On!, you have to be aware that this is not the sort of thing you read to see the story go anywhere. Each chapter is self-contained and there is no overarching storyline. K-On!'s main strength is it's strong characterization. Those who enjoy K-On! to its fullest are the ones who get attached to the characters. Once you get in the proper mindset, K-On! is a funny and cute series that really pulls the reader into its world. It exemplifies the concept of "feel good". Unless you're trying to be a grump, by the end you will feel cheery.
K-On! is probably my favorite Japanese franchise in years. The author (kakifly) has a strong talent for characterization. This is not a story about conflict and resolution, it's a slice-of-life. That said, I don't think I've read anything that does the genre better.