Direct characterization is when the author explicitly states details about a character to help build knowledge of that character's personality, motives, or appearance. Indirect characterization, by contrast, is when the author provides information and asks readers to make inferences about a character.
Let's first examine Moishe the Beadle, who appears in chapter 1. Wiesel writes that Moishe is "poor" and that he is "awkward." He also has "wide, dreamy eyes" and enjoys singing. All of these are examples of direct characterization. Through these details, readers learn more about Moishe without having to make any inferences; the details are straightforward. Later, Wiesel recalls that after asking Moishe why he prays, the man "spoke to [Wiesel] for hours on end about the Kabbalah's revelations and its mysteries." In this statement, readers learn more about Moishe, but some inference is required in order to do so. Moishe clearly values his faith and believes that it is worthwhile to take the time to teach a child the importance of prayer. He is also knowledgeable and well-versed in the intimate details of his faith, speaking on one key topic for "hours." These inferences are examples of indirect characterization.
Both direct and indirect characterization are used to describe Mrs. Schachter in chapter 2. Wiesel uses direct characterization to convey that the woman is "in her fifties" and that she is a mother traveling with her ten-year-old son. She is "quiet" and "tense," with "piercing eyes." She has often visited Wiesel's home, and she has financially supported her family so that her husband could devote himself to studying.
Readers learn more about Mrs. Schachter through indirect characterization. Wiesel finds Mrs. Schachter and her son inside the cattle car, en route to a concentration camp. None of those trapped in the cars have yet heard of Auschwitz; however, as they travel, Mrs. Schachter screams about the "fire" she sees. No one else can see any evidence of flames, and the other passengers forcibly silence her. Yet she continues to point into the distance, yelling about the "fire, over there!" Readers who have knowledge of the horrors of concentration camps can make some inferences here. Nazis frequently murdered Jews whom they deemed unfit for labor, including the very young, the very old, and the physically challenged. Massive crematoria were constructed at Auschwitz-Birkenau to burn human bodies. Thus, Mrs. Schachter was describing a kind of prophetic vision, somehow able to see things which had not yet come to pass in her life. Though the passengers with her inside the cattle car deemed her a madwoman, she was actually more realistic in her vision than those who believed that the camps would not separate families and would protect the old and the sick. Recognizing the prophetic abilities of Mrs. Schachter requires some inference, which means this moment stands as an example of indirect characterization.
I hope this helps as you consider other instances of characterization in these chapters. Good luck!