Elie Wiesel wrote Night as an adult, but he wrote it about his experiences when he was a teenager. Growing up is difficult enough without adding the horrors of the Holocaust; growing up in the middle of this horrific time simply intensified the experience for Elie.
One thing that happens as we all grow up is that we begin to be independent from our parents. Though Elie is dependent on his parents like every other person his age, there comes a time when Elie begins to detach from his father (his mother and sister are gone before he can even think about detaching from them). This is intensified in the concentration camps because it truly is "every man for himself" when it comes to survival.
Another thing that naturally happens as we grow up is that we begin to be self-sufficient. While it is true that, in Elie's case, he is not working for money, he is forced to rely on himself to survive--and since he does survive, he can consider himself successful at this.
The most significant and potentially damaging element of growing up is learning that life is not exactly what we thought or believed. We grow disillusioned when we discover, for example, that our parents are not always right or that the people we love do not always love us back. In Elie's case, the disillusionment is crushing.
Elie is a Jew and he grew up with more sensitivity to spiritual things. When the concentration camps, which are primarily filled with Jews, become Elie's reality, he finds it difficult to maintain his faith. He does not understand how, if God loves the Jews as He said He did, He would allow such atrocities to happen to them. On his first night at Auschwitz, Elie says this:
Never shall I forget that night, the first night in camp, which has turned my life into one long night, seven times cursed and seven times sealed....Never shall I forget those moments which murdered my God and my soul and turned my dreams to dust. Never shall I forget these things, even if I am condemned to live as long as God Himself. Never.
It is this loss of faith, both in man and in God, which marks Elie's most significant transition from a boy to a young man. He has "grown up," but there is no pleasure in the experience because his innocence has been stripped from him.