From Chabad @
http://www.chabad.org/parshah/in-depth/default_cdo/aid/39684/jewish/In-Depth.htm
And Nadav and Avihu, the sons of Aaron, took each of them his censer... And they died before G-d (10:1-2)Bar Kappara said in the name of Rabbi Jeremiah ben Elazar: Aaron's sons died on account of four things: for drawing near, for offering, for the strange fire, and for not having taken counsel from each other. "For drawing near"--because they entered into the innermost precincts of the Sanctuary. "For offering"--because they offered a sacrifice which they had not been commanded to offer. "For the strange fire"--they brought in fire from the kitchen. "And for not having taken counsel from each other"--as it says, "Each of them his censer," implying that they acted each on his own initiative, not taking counsel from one another.
Rabbi Mani of She'ab, Rabbi Joshua of Siknin, and Rabbi Yochanan in the name of Rabbi Levi said: The sons of Aaron died on account of four things... Because they had drunk wine, as it says [immediately following the incident], "Drink no wine nor strong drink... that you die not" (Leviticus 10:9). Because they served in the Sanctuary lacking the prescribed number of priestly garments (cf. Exodus 28:43). Because they entered the Sanctuary without washing their hands and feet (cf. Exodus 30:21). Because they had no children... as it says, "And Nadav and Avihu died... and they had no children" (Numbers 3:4).
Abba Hanin says it was because they had no wives, for it is written [regarding the High Priest], "And [he shall] make atonement for himself, and for his house" (Leviticus 16:6)--"his house" refers to his wife.
Rabbi Levi says that they were arrogant. Many women remained unmarried waiting for them. What did they say? Our father's brother is a king, our mother's brother is a prince [i.e., Nachshon, the head of the tribe of Judah], our father is a High Priest, and we are both Deputy High Priests; what woman is worthy of us? ... Moses and Aaron went first, Nadav and Avihu walked behind them, and all Israel followed, and Nadav and Avihu were saying: "When will these two old men die and we assume authority over the community?" Rabbi Judah in the name of Rabbi Aibu said that they uttered this to one another with their mouths, while Rabbi Pinchas said that they harbored the thought in their hearts.
Others say: They already deserved to die at Mount Sinai, when they callously feasted their eyes on the Divine (Exodus 24:9-11).
(Midrash Rabbah; Rashi)
Rabbi Eliezer ben Yaakov stated: The sons of Aaron died only because they gave a legal decision in the presence of their master Moses. What was the exposition they made? They interpreted the verse (Leviticus 1:7), "And the sons of Aaron the priest shall put fire upon the altar." This is to teach us, they said, that although fire came down from heaven, it is nevertheless a mitzvah to bring also ordinary fire. (This is indeed the law; their sin was that they rendered a Halachic decision in the presence of their teacher.)
(Talmud, Eruvin 63a; Rashi)
Nadav and Avihu died because of Aaron's making of the Golden Calf, as it is written: "And against Aaron did G-d verily rage to destroy him; and I prayed also for Aaron at that time" (Deuteronomy 9:20). "To destroy him" means the death of children, as it is written, "And I destroyed his fruit from above" (Amos 2:9). Moses' prayer was halfway effective, so that two died and two remained alive.
(Rashi on Deuteronomy 9:20)
"They came close to G-d and died" (Leviticus 16:1)--they approached the supernal light out of their great love of the Holy, and thereby died. Thus they died by "divine kiss" such as experienced by the perfectly righteous; it is only that the righteous die when the divine kiss approaches them, while they died by their approaching it... Although they sensed their own demise, this did not prevent them from drawing near to G-d in attachment, delight, delectability, fellowship, love, kiss and sweetness, to the point that their souls ceased from them.
(Ohr HaChaim)
And a fire went out from G-d and consumed them (10:2)But subsequently it says that Moses instructed Mishael and Eltzafan "Carry your brothers from before the Sanctuary" and that "They carried them out in their robes"? ... G-d sent forth two threads of fire into each one's nostrils and consumed their souls, without touching their flesh and without touching their clothes.
(Midrash Tanchuma)
And Moses said to Aaron: "This is it that which G-d spoke, saying: I will be sanctified in those who are close to Me..." (10:3)This was said to Moses at Sinai, but its meaning was not known to him until the occurrence happened, when Moses said to Aaron: "My brother, at Sinai, G-d said to me: 'I will sanctify this House, and through a great man would I sanctify it,' and I thought that either through me or through you would this House be sanctified; but now I see that your two sons are greater than you or I."
(Midrash Rabbah; Rashi)
And Aaron was silent (10:3)Because Aaron was silent, he was rewarded that G-d spoke exclusively to him (see below, verses 8-11; ordinarily G-d spoke to Aaron only in conjunction with--or through--Moses).
(Midrash Rabbah)
Said Rav Papa: The merit of attending a house of mourning lies in the silence observed.
(Talmud, Berachot 6b)
In youth, one learns to talk; in maturity, one learns to be silent. This is man's problem: that he learns to talk before he learns to be silent.
(Rabbi Nachman of Breslav)
Speech signifies comprehensibility. Melody is beyond language, expressing moods which words cannot describe. Silence is yet higher.
The power to be silent at certain moments of life and of history is an important strength. It expresses the awareness that G-d is infinite, and cannot be encapsulated in our human conceptions of what should take place.
The Talmud tells of an instance in which Moses himself was told by G-d to be silent. G-d showed him in a vision all future generations of the Jewish people, and the leaders of each generation. Moses was greatly impressed by the wisdom of Rabbi Akiva. Then he saw the way the Romans tortured him to death. "Is this the reward of his Torah knowledge?" Moses asked. G-d answered: "Be silent. Thus it arose in My thought".
This is not to say that the Torah advocates a fatalistic approach to life. Before the event, one must do everything possible to prevent tragedy. But once it has happened, G-d forbid, through the acceptance and the silence we reach a special closeness to the Divine. Our Sages tell us that because Aaron was silent, he was rewarded by G-d speaking directly to him.
In our generation, too, there is a need for this power of silence. It is not a passive power, but one that leads to vigorous and joyous action. The Jewish response to the harrowing events of the Shoah is the determined and energetic action to rebuild Jewish family life and Jewish knowledge.
Through our power of silence we too, like Aaron, will merit Divine revelation. G-d will bring the Messiah, rebuilding the Temple and bringing lasting peace to the world.
(The Lubavitcher Rebbe)