Lyric discussion by newsies234 

Cover art for Mermaid lyrics by Regina Spektor

I think the above people have covered the meaning pretty well. She's gotten rid of what made her unique so that she could fit in, but fitting in isn't all it's cracked up to be.

Also, where the lyrics say "no matter how clean," I think she says "no matter how I plead" or, at least, that's what she says in the version I've heard.