I would say that a large reason why Elie Wiesel composes his work is to engage in the process of remembrance and reclamation. One of the most striking realities of something as horrific as the Holocaust is the idea that it was so awful and so brutal, that in order to move on, one must put it aside and deep into the recesses of one's experience. While logical to a certain extent, this idea neglects the fact that in doing so, one is still a victim and not in control of what happened. In tracing the origins of the work, Wiesel was speaking with a colleague about how people reacted when Jesus was crucified. In a moment of psychological tangency, Wiesel rebuked his friend with the response of how few spoke out about the Holocaust. Wiesel's colleague understood the origins of such a comment and told him to break the silence with the writing of his memoirs. In this moment, one sees why Wiesel seeks to remember the Holocaust. The book is his memoir, but it is also his psychological attempt to reclaim a voice out of silence. The work seeks to remember the Holocaust in order to not remain in silence and to speak regardless of what others do. This becomes critical in both asserting voice and also in exercising autonomy. Surviving is not no longer the primary essence for Wiesel, as it was during his time in multiple camps, but rather living, as he has progressed from his tenure under the horrific shadow of the Holocaust. In 1999, Wiesel delivered a speech at the White House entitled, "The Perils of Indifference." In the speech, Wiesel argues that silence acts as a "nod to the aggressors." In these words, one fully understands why Wiesel writes his work, speaks his mind, and continues to actively serve as history's conscience: In silence, one emboldens those who have done terrible things. In speaking, we force accountability and moral responsibility. This would be why Wiesel remembers the Holocaust, and activates his voice and humanity for all of us to attempt to model in our own lives.
The idea of remembering tragedies may sound like something odd, but there is a great reason for it. To remember tragedies allows one to have a realistic picture of life, namely, that evils take place and that people are capable of both sublime things, but also horrible things as well. Therefore, to remember these things acts to check the tide of evil, so that things like the holocaust would not happen again. Also by remembering, you also honor the memory of those who died. If you read many great traditions of thought, they will say the same thing.
In this Nobel Peace Prize speech, Elie Wiesel said that if we forget "we are victims, and we are accomplices" and that he would never forget what happened because through remembrance we both honor and learn, love and hate, and become all the more human in the eyes of the world.
You can read all about it in the transcript for his Nobel Peace Prize Acceptance Speech. He explains it all there.
Initially after enduring the horrible conditions in the ghettos, mistreatment of the Jews and other unwanted citizens, horrors of the concentration camps, and the death of his family members, Elie Wiesal sought to be silent and to try and not face the issues that haunted him. However, after discussions with friends he began to realize that unless the atrocities continued to be in the minds of men, they could continue to look away. If mankind looked away from similar situations the same thing could happen again.
Wiesal had never expected that humanity could be so cruel and that nations of people would do nothing to help people who were so badly mistreated. He knew that they had not done anything wrong. Men, women, and children had been allowed to experience torturous situations and death because people had looked away.
Wiesal wrote his book "Night" and several others to demonstrate to mankind what atrocities men were capable of committing. He also wanted his books to serve as a witness and testament to the experiences of the Jews and people the Nazi government considered to be waste products. His desired outcome was that by writing of his experiences he could prevent future generations from making the same mistakes. He thought if the truth stayed hidden it would happen again. His truth was mean to help others to feel inspired to take action and prevent such occurrences from ever happening again in our world.
Unfortunately, it has happened again to the people of Dafur and other countries due to the concept of ethnic cleansing. When the Taliban took over in Afghanistan the process also occurred. Man's nature stills hides within. The work of Eli had not been created in vain though as it has been used by groups that have rallied together to raise public awareness, funding, and resources to try and protect the citizens in other lands who are being or have been harmed due to ethnic cleaning. There are other countries where ethnic cleansing has occurred and may still be occurring.