I came to enjoy the show because the characters are just simply fun to watch. There really isn't a major over arching plot to this. Just some Japanese girls in high school who form a school band that are the focus of an anime in which the endings of the show will tease you.
I originally thought K-On was a show about a group of High School girls who make it big as a band and go on to be a more light-hearted version of Nana, an anime that I believe I watch 3x+ episodes of before accidentally dropping it. I never really got into K-On until I stumbled upon this picture of Sawako which drove me into finding out who the artist was and then anime the character was from(Toten for those who want to know)
I stumbled across a K-On wiki entry on Sawako and, as you could imagine, was a bit let down by the original characters design. That is until I scrolled down a bit and found the entries other pictures of Sawako and then promptly went on to read the page, got intrigued by the character, and went on to go watch K-On (First Season and Second season were over by the time I took interest).
I found myself vastly in awe with the show. Never in the years I had been watching anime and reading manga had I ever sat down and, with intent, watch a slice of life anime. I had always searched for the next big action anime of some form with guns and super powers. I never would have thought that I would be watching an anime because a bunch of characters are just having a real good time being friends and trying to solve the Earth destroying problem of what type of cake should be had on this day.
I look back at K-On and think to myself, "I would like to see more of this. K-On was really special." K-On is not the Holy Grail of Awesome. It's just a show that if you get into you will find yourself falling in love with, hopefully without the need to lick your monitor or to create a shrine in the name of Mio.
The whole basis is that K-On is just a simple slice of life anime with girls who just can't stop being cute and making me laugh. It also is probably one of the many anime's that you could probably show to a highly rational person and... umm. You know what, this is one of those anime's I'd show to my mother because she would enjoy this as well.
Now if you excuse me, I have to investigate the freezer.