I make the case here that our love of music doesn't need a reason to exist. At least I hope it does'nt, since I'm living this very theory.
My absolute favourite band is Radiohead. I've followed their career since turned on to them by a friend in High School. They've alienated the majority of their fans with their latest records, but I'm still a die-hard fan. Their album that was released in 2007 (In Rainbows, for those not obsessed with Radiohead or willing to click the link) is my current favourite, although I change this stance a fair bit (here's their whole discography - I'm sure most have spent some time in the coveted favourite spot).
When talking to my wife about a song recently, I voiced the fact that I had no idea what the words were. Then, I thought a bit, and I think I might understand the words to 10% of Radiohead songs. Of those 10%, I understand the meaning behind 0% of the songs. I just love em.
My absolute favourite song of theirs (Paranoid Android, for those making a list.... creepy), I completely melt every time I hear it due to its sheer awesomeness. The video is potentially better than the song alone, which is high praise. Just don't ask me why either the song or the video is awesome.
Do you have any bands whose tunes you just DIG, but don't understand?