It is not completely clear what "Kyrie Elieson" stands for. In the context used by the song, you might expect "Kyrie Elieson" to be a name. However, the only thing I found suggests that the name should be "Kyrie Eleison". (The name used here is what is on the CD inserts.) That is Greek for "Lord Have Mercy". However, "Lord Have Mercy" does not fit the rest of the lyrics well. You can discuss the name further here.