The question is a little confusing: "What was Eliezer's importance in Night." The confusion stems from the fact that "Eliezer" and "Elie Wiesel," the book's author, are the same person. "Elie" is a shortened form of "Eliezer." As Night is Wiesel's memoir of his time in German concentration camps, from which vantage he observed first-hand the systematic extermination of Europe's Jewish population, an event known as the Holocaust, his importance to the book cannot be overstated.
Night, as noted, is Elie Wiesel's recollection of his and his father's horrendous experience in the concentration camps that served as both a means of cheap forced labor for German industry and as vehicles for the slaughter of those deemed too weak to work. That chimneys are the defining characteristic of those camps is no accident, as to be thrown into the ovens of Auschwitz, dead or alive, was a common theme of Germany's racial policies. In the event that somebody needs affirmation from the text of Wiesel's book that he is "Eliezer," one need read no further than the author's preface to the 2006 edition of a memoir originally published in 1958:
"I remember that night, the most horrendous of my life: '…Eliezer, my son, come here… I want to tell you something…Only to you… Come, don't leave me alone…Eliezer…'"
Wiesel, in this passage, is describing the emotional torment that will haunt him to his death, the anguished words of his father, who, unlike the son, would not survive their shared ordeal.