Lyric discussion by MemoryWake 

Cover art for SW lyrics by Blonde Redhead

This line captures the meaning of the song pretty clearly:

"It's not, it's not what it seems ... It's not what it seems."

The song is about how the external life can differ from the internal life--it's not what it seems. He is not what he seems. His actions are not what they seem. It's the meaning behind his actions that is essential to who he is--the overt can obfuscate the truth.

"It's not, it's not what you give but it's what you kept It's not, it's not who you kill but it's who you left"

^Looking at the actions of this person will not lead you to the correct insight about who he is--you can observe what a person gives in a relationship and who a person hurts, but it's not as obvious what a person keeps for themselves and doesn't share with others (and why) or the root of the personality traits that lead him to harm someone else years later.

"It's not, it's not how you speak but it's what you said. It's not, it's not what you seek but it's what you have."

^This person's delivery is at odds with the intent of his speech, which is to say that this is someone who hides his true intentions under a seemingly lovely patina. To see the truth about him, you need to look at the results he is trying to elicit despite the flowery language. Words are being used to conceal thoughts. The second line is a little less clear, a little more potentially nuanced. I actually think it's from the perspective of the guy described, saying that this life isn't what he wants, but it's what he has.

And then the repeated stanza is from the man's perspective:

"I am I am running in my head I am I am lying on my left I am I am growing in my bed I am I am..."

^Same meaning, from his perspective. His body is in bed, his intentions and thoughts, however, are diametrically opposed to what his physical form might be doing. You can't look at this guy's overt self and understand him or know him; the truth about who he really is and what he really wants is... not what it seems.