Our Parsha begins by referring to an episode originally recorded in Parshas Shemini, namely, the deaths of Nadav and Avihu (ויקרא ט"ז:א'). Aharon had four sons, two of whom were Nadav and Avihu. According to Chazal, they were not only handsome, but also gifted with outstanding abilities. In addition, their righteousness was of such caliber that they were obviously qualified to become the future leaders. Their greatness is in fact indicated in their very names. The name "Nadav" signifies nobility and purity, as in the Korban Nedavah, a free-will offering unto Hashem which represents those concepts. The name "Avihu" implies that this person was worthy of being the "Av," the father, or leader, of the Jewish people.
Not only was their spiritual level considered higher by others, but they themselves were conscious of their abilities. This unfortunately led, however, to their downfall. The Midrash tells us that while walking behind Moshe and Aharon, Nadav once remarked to Avihu, "When will these two elders finally depart from the world so that we may assume leadership of the community?" Hashem answered, "We shall yet see who shall bury whom!" Nadav and Avihu thus died themselves long before Moshe and Aharon did.
It must be understood that according to Chazal, Nadav and Avihu were Tzaddikim. The meaning of their words cited above was, "Moshe and Aharon are old and will certainly die soon. We will then be called upon to assume the leadership and who knows if we are fit." Nonetheless, their attitude was inappropriate. Chazal worded their remark in the above drastic manner to point out that they referred to their future roles as leaders. A certain lack of humility was present in their attitude and mode of expression.
On the eighth day of the inauguration of the Mishkan, the Heavenly fire descended and consumed the sacrifices (שם ט':כ"ד). Following this event, Nadav and Avihu decided that it was nevertheless correct that they should place their own fire on the Mizbeiach. They inferred this Halacha from the Posuk earlier which says that the sons of Aharon the Kohein shall put fire on the altar (שם א':ז'). Since both Nadav and Avihu were great Torah scholars, they deduced from this Posuk that it was a Mitzvah to put fire on the altar despite the fire from above. But, they formulated this Halacha in Moshe's presence, as Rashi (שם י':ב') says, and thus, although their Halachic decision was correct, as indicated by Rashi in Yoma (דף נ"ג. בד"ה מצוה), they deserved the heavenly death punishment because they were forbidden to decide a Halacha in the presence of their Rebbe, Moshe, without consulting him. Without proper humility, Torah can not be learned and Judaism can not survive.