The title is so central to the poem that English translators of the poem can't quite agree on what it should be. Some people prefer a translation of the original title in Romanian, "Death Tango." According to one critic, at a concentration camp near Celan's birthplace, "Jewish musicians were ordered to play a 'Death Tango' during marches, grave-digging, tortures, and executions" (source). But when he translated his own poem into German, Celan changed the title to "Todesfuge." In English grammar this would be "Death Fugue," but the translation we prefer uses "Deathfugue" to capture more of the essence of the German language.
A fugue is a musical piece that begins with a theme and then restates that theme several times with variations. The fugue is most closely associated with J.S. Bach, a German musician who was one of the greatest composers who ever lived. Bach's fugues could get crazy-complicated, to the point that he embedded his own name in musical notes: B-A-C-H. One of his most important works is called "The Art of the Fugue." The title of Celan's poem, then, refers both to the music played by the prisoners in the poem and also to the repetitive form that Celan uses throughout.