A euphemism, of course, is a positive (or indirect) word that is used instead of a negative (or direct) word when referring to something especially harsh or horrible.  The best examples of euphemism in The Boy in the Striped Pajamas involve the theme of innocence in regards to the character of Bruno.  Probably the most important euphemisms in the book are "Out-With" and "the Fury." 

As the young son of a Nazi commandant, Bruno is innocent of the horrors going on around him.  As a result, Bruno uses words that are euphemisms to the ears of the reader in order to label the name of the Nazi concentration camp and the name of the German leader.  Bruno's euphemism for the famous Nazi Concentration camp called Auschwitz is Bruno's milder term "Out-With." This euphemism is also ironic in that Jews are often killed or "outed" within this concentration camp.  It is yet another irony that Bruno is "outed" himself after donning the "striped pajamas."  

A second euphemism is a reference to the self-proclaimed label of Adolf Hitler, otherwise known as the Führer (in order to seem scarier).  Bruno innocently calls Adolf Hitler "the Fury."  This takes some of the fear away from Adolf Hitler's title.  Further, Bruno immediately dislikes Hitler; however, Bruno is not quite sure why.  The other irony here is similar to the irony stated in the previous paragraph.  It is Hitler's "fury" or anger that has caused him to hate the Jews and put them into these camps.

These euphemisms can also serve as dramatic irony (when a character does not understand something that the reader does understand).  Bruno has no idea of the true meaning behind the euphemisms he uses.  In fact, they are simple mispronunciations of the negative terms used in Nazi Germany.