Siren songs are mythical songs sung by sirens, creatures from Greek mythology. The songs were said to be so beautiful and enchanting that sailors would be lured to their deaths upon hearing them. The term 'siren songs' can also refer to any type of song that is seductive and alluring. The crossword solution for the term 'siren songs' is 'WAILS, ' which accurately describes the sound of the mythical siren songs.