Legend has it that this was the final song played by the orchestra as the RMS Titanic sank. The melody is a beautiful one, and its beauty of the song lends this portion of the movie a weighty poignance. I don't care for "Titanic," but this scene did teach me to love "Nearer my God to Thee." I love the moment of acceptance in the eyes of the first musician, and then as it spreads to his fellow players as they join him.
Their music is an act of communion as they see death slowly rising up the deck of the ship, and it compares well to the grace and acceptance of the other passengers on the ship: the mother who tells her children one final bedtime story, about living forever in the land of Tír na nóg; the elderly couple as they calmly wait for death, together in bed; the ship architect who is weighted down by conscience over his failed enterprise; the quiet despair of the ship's captain as the unthinkable unfolds around him and Death presses against the helm; and of course the loud and panicked despair of the crew and passengers as they realize there will be no escape.
There are lyrics, of course; and there are many videos available where they are capably sung. But thanks to the beauty and grace of this scene, those feel almost superfluous. Played well on strings, this tune has a staying power all of its own.