There are different kinds of music listeners. 
I am the kind of music listener who listens primarily to the melody and the atmosphere of the song before I ever ascertain the lyrics. Sometimes the lyrics are very clear to me and sometimes I can go years without really knowing what a song is about, then when I realize what the song is really about it's a revelation.
For example, there's a Smiths song called "This Night Has Opened My Eyes." It has a pretty, muted, mysterious quality about it, and the lyrics never particularly called attention to themselves. Then one night my eyes were opened:
 In a river the color of lead
 Immerse the baby's head
 Wrap her up in the news of the world
 Dump her on a doorstep, girl
 This night has opened my eyes
 And I will never sleep again
Basically it's a song about getting rid of a baby. How could I not have noticed that? I just thought it was a pretty song about someone having a revelation about something, some night. 
Another song I recently realized the lyrics for is The B-52's song "52 Girls," which is much more whimsical.
 Effie, Madge and Mabel, Biddie
 See them on the beach or in New York City
 Tina, Louise and Hazel and Mavis
 Can you name, name, name, name them today? ...
 These are the girls of the U.S.A.
I always knew they were singing girls' names, but I never knew the song was actually about girls' names.
Last night I heard a band cover The Cure's "Just Like Heaven."
 "Show me show me show me how you do that trick
 The one that makes me scream," she said
 "The one that makes me laugh," she said
 And threw her arms around my neck
 "Show me how you do it
 And I promise you I promise that
 I'll run away with you
 I'll run away with you"
And then the girl goes away, either into the sea, or into the ocean "deep inside of" the narrator...
In moments like this, I wonder how much of life I'm just blatantly oblivious to... 
So much ignorance...
So much to discover...