And, if you want to go to the root document for the song (Psalm 137), here it is from the King James version:

Psalm 137

 1By the rivers of Babylon, there we sat down, yea, we wept, when we remembered Zion.

 2We hanged our harps upon the willows in the midst thereof.

 3For there they that carried us away captive required of us a song; and they that wasted us required of us mirth, saying, Sing us one of the songs of Zion.

 4How shall we sing the LORD's song in a strange land?

 5If I forget thee, O Jerusalem, let my right hand forget her cunning.

 6If I do not remember thee, let my tongue cleave to the roof of my mouth; if I prefer not Jerusalem above my chief joy.

 7Remember, O LORD, the children of Edom in the day of Jerusalem; who said, Rase it, rase it, even to the foundation thereof.

 8O daughter of Babylon, who art to be destroyed; happy shall he be, that rewardeth thee as thou hast served us.

 9Happy shall he be, that taketh and dasheth thy little ones against the stones.

I'm not much of a Biblical scholar, but I think reading the Psalm gives some understanding of the pain and anger of exile and the longing for home that is at the heart of both the Psalm and the song.

Ward