From the first chapter of The Boy in the Striped Pajamas, Bruno is already aware that his father is a "man to watch" and is very important because he has seen how "visitors" treat his father and are deferential to him; soldiers and typists are particularly polite. Bruno's mother tells Bruno that his father has been tasked with doing "a very special job" which is why they have to move; something she is not happy about. Bruno admits to himself that he does not really understand his father's job to the point that he cannot explain it to others; unlike his friend Karl whose father is a greengrocer, something he can easily understand. He knows that his father is now a commandant, after a recent promotion, but he does not know what that infers and in chapter 7, Bruno congratulates his father on his new job without understanding anything more than smart uniforms and Bruno's father having made his grandfather very proud.  

In chapter 2, the family arrives in "Out-With" (Bruno's mispronunciation), and Bruno cannot believe that he will have to live in such a "desolate" place. He wants the family to return home to Berlin and becomes angry at more talk of his father's job when it is quite clear to Bruno that "Father should think twice about his job" (chapter 2). Bruno feels that he should voice his opinion because even though fathers are supposed to be "serious," and he says that "it doesn't matter whether they're or greengrocers or teachers or chefs or commandants," Bruno still recognizes that this is all a "bad idea."

Bruno decides to speak to his father about moving back to Berlin and wonders whether Father did something "that made the Fury angry" (chapter 5). Bruno knows that his father works for the (mispronounced) "Fury" ("a great leader" as he's described in chapter 11)  and that the "salute" is a very significant part of showing respect and he wonders why anyone would send his father to such a terrible place. In chapter 6, Bruno discusses the situation with Maria, the maid, and tells Maria that he doesn't think he trusts his father's judgment anymore but he does not understand what his father's job entails.

Even when he speaks to Shmuel, who dislikes soldiers, Bruno quickly defends his father; even wanting to be like him, "one of the good soldiers" (chapter 13). In chapter 16, Bruno is aware of his father's smart uniform "with the decorations" but he will still never understand what his father actually does. In chapter 19, even as Bruno stands among the people on Shmuel's side of the fence, after they have been called to march, Bruno wants to reassure them that marching is not so bad and that his father is  the Commandant so "it must be alright." He has no idea that moments later he will stand in the gas chamber and never be seen again. 

In The Boy in The Striped Pajamas, why doesn't Bruno understand his father's job?

The Boy in The Striped Pajamas reveals the disparity between appearance and reality. To Bruno, his father is "one of the good soldiers" who has "an impressive uniform and ...everyone calls him Commandant and does whatever he says." Bruno does notice his grandmother's displeasure at her own son's occupation but Bruno puts everything into his own context and sees only one perspective. He sees the armbands and muses over whether he would prefer to wear one like his father's (the swastika) or one like Shmuel's (the star), feeling a little offended that no one has ever asked him if he would like to wear one. Because of the protected environment he has grown up in, Bruno can't even make sense of what Shmuel says, thinking he must be exaggerating and "he didn't really believe that eleven people could live in the same room together." Bruno cannot imagine a cruel world or actions that have no logical reason so he takes everything at face value.

Bruno's questions that he poses to his father, are always avoided or answered vaguely and unsatisfactorily but there is not much he can do about it and he forms his own opinions based on his limited understanding. He is forbidden from exploring - one of his favorite occupations - with "No exceptions"- but has no idea what his parents are trying to protect him from. His parents' lack of communication is what will eventually lead to his death as he innocently joins Shmuel on the "other side of the fence" and seals his fate.