It is very significant. The title of the book refers to the fear and safety that the cover of night brings. Night is the time when the SS came for the prominent Jews in the communities both before the Jews were evacuated to the concentration camps and also in the camps themselves. In this regard, night was a time to be feared since you couldn't see what was coming. In the book, the victims of the concentration camps could let down their guard a little at night where no one could see them, and they could cry or not be so careful with facial expressions. In this regard, night was a time of comfort and relaxation. It was a cruel, double-edged sword.
One important quote in the book which really points to the purpose of the title is:
Never shall I forget that night, that 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. Chapter 3, page 32.
I am not sure I interpret the quote: "Never shall I forget that night..." in the same way. This is the first moment in Wiesel's memoir where Wiesel realizes the importance of questioning God. He begins to question God, which he later deems a religious act in and of itself, at Night. Further, this quote suggests that Wiesel realizes the importance and truth of night. Wiesel previously questioned why it was important for Moshe to have the people of Sighet believe his stories of the first deportation; Wiesel now realizes the truth that night holds. This develops throughout Night but is greatly expanded upon in Dawn.
I do not believe that Night and Dawn should be separated if students are to understand Wiesel's central theme. I spend a great deal of time with my students discussing the difference between a memoir and a novel. While Dawn has a central, fictious character named Elisha, many parrallels can be drawn to Wiesel himself. Ultimately, all "victims" must re-integrate into society; in the wake of tragedy, one questions God, but also his/her role in fighting against his/her oppressors: should we "fight" through retaliatory murder or through words?
As English teachers, we can discuss the inherent power of language and why Wiesel selects writing as his mode of retaliation.
But to return to your initial question regarding a quote that explains the importance of Night...let's turn to Dawn. I highly recommend reading this to fully understand the theme conveyed through Wiesel's analysis of night and eyes.
Beggar: "I'm going to teach you the difference between day and night. Always look at a window, and failing that look into the eyes of a man. If you see a face, any face, then you can be sure that night succeeded day. For believe me, night has a face" (4).
Wiesel, Elie. Night. New York: Bantam, 1982.
There are many more quotes that support this, however, my annotated text is sitting on my desk at school.
Ultimately, the main character must make the most important decision of his life at night. Even though he does not "hate" Captain John Dawson, he chooses to execute him. By doing so, he, in fact, "kills" himself. This realization comes at Dawn--through the night, we search for truth.
Essentially, Wiesel shifts the burden from God to a burden on man. Man has done this to man, and it is man's responsibility to put an end to hostility. It is man who must save humanity. You may also want to read the prefaces in the most recent edition to both Dawn and Night; the edition is translated by Wiesel's wife from Yiddish. Further, I discuss Wiesel's Nobel lecture "Hope, Despair, and Memory" with my students.
An aside: I have not taught The Accident, or Day, in conjunction with Night and Dawn though it is the final book of the trilogy. I am still working through my analysis of this text.