What are key phrases or quotes from The Boy In the Striped Pajamas by John Boyne?

There are many important quotations from The Boy in the Striped Pajamas. First, let us look at a few that have to do with the characterization of Bruno and the theme of innocence.

What exactly was the difference? He wondered to himself. And who decided which people wore the striped pajamas and which people wore the uniforms?

This quotation shows Bruno (in all of his innocence) revealing true wisdom.  Bruno is speaking about the "difference" between the Jews imprisoned in Auschwitz, the soldiers under Hitler's control, and young Germans like Bruno. The beauty behind Bruno's words here is that there really is not a difference at all. They are all people worthy of love, respect, and friendship.

We're not supposed to be friends, you and me. We're meant to be enemies. Did you know that? 

This quotation is spoken by Bruno to Shmuel.  It reveals Bruno's innocence.  It also contains the realization that, according to Hitler, Germans and Jews are never supposed to be friends.  It is also the reason why Bruno immediately parrots that he is "superior."  

Next we should look a two quotations that reveal the purpose behind the book.  The first looks at the theme of friendship and how this type of love can transcend all boundaries.

He looked down and did something quite out of character for him: he took hold of Shmuel's tiny hand in his and squeezed it tightly.  "You're my best friend, Shmuel," he said. "My best friend for life.” ... Despite the mayhem that followed, Bruno found that he was still holding Shmuel's hand in his own and nothing in the world would have persuaded him to let go.

These are Bruno's and Shmuel's last moments.  The two best friends are holding hands and walking into the gas chamber to their deaths.  Willing to die for each other, the two face death together because of their great friendship.  This power behind this friendship theme is one of the purposes behind this book.  Friendship can transcend all obstacles.

Their lost voices must continue to be heard.

Finally, we come to another quotation that reveals a purpose of this novel:  to give a voice to the lost people of the Holocaust.  Many of these lost people were Jews from Poland, just like Shmuel and his parents.  In writing a book like this, John Boyne makes sure that these lost voices are, in fact, heard.