I believe this song can be taken two ways.
1) Lynn is talking about a lover she only keeps around so she doesn't have to feel lonely. This other person doesn't feel anything, but gives her a sense of comfort and companionship because she is the same type of person.
2) Lynn could also be talking about herself. She stands before a mirror trying to find herself. And every night at midnight, she dreams about leaving her own body. Her inner self, like the lover from the first theory, doesn't feel anything. There's no love, compassion, happiness, or anything. She talks about her inner self being dead inside, but making her feel alive in her inner self's presence.