What does "K-On!" refer to in the series?
"K-On" is pronounced the same as the word 軽音 keion, which means "light music" (in the Japanese sense, not the classical sense). The main characters are, of course, part of the light music club, which is the 軽音部 keion-bu. The "K-On club", if you will.

If you had watched it with Japanese audio, you would have probably noticed the word sprinkled all over the place (since they talk about the club a lot, obviously). The eyecatches (I forget for which season) also have audio of Yui saying "K-On". I suppose they must have changed the eyecatches to something else for the English dub.