The following is not my interpretation. I found the information at SongFacts. Here's the link: Hallelujah by Jeff Buckley Songfacts
The song is about love which has soured and gone stale. Cohen used a lot of religious imagery, including references to some of the more notorious women in the bible. Here's some lyrical analysis:
"You saw her bathing on the roof, her beauty and the moonlight overthrew you" - Bathsheba, who tempted the king to kill her husband so he could have her.
"She tied you to her kitchen chair, she broke your throne and she cut your hair" - Delilah, who cut off Sampson's locks that held his superhuman strength.
"But remember when I moved in you and the holy dove was moving too" - This could be a reference to the divine conception and Mary.
The lines referring to the immaculate conception can also be interpreted as having a sexual connotation: "And every breath we drew was hallelujah."