Sons of Aharon Hakohen.
In Shaar HaGilgulim (hakdamah 31) of The Ari, Rabbi Yitzchak Luria states that the souls of Nadav and Avihu came from a very high level of Adam. The level of Nefesh of Atzilut. After their death they returned again as an ibur ( A new [higher] soul coming into a person while he is still alive) in Pinchas son of Elazar son of Aharon Hakohen.
For the purpose of correcting their soul Nadav and Avihu returned again as an ibur or gilgul in Eliyahu Hanavi (Elijah the Prophet), Shmuel Hanavie (Samuel the Prophet), Elisha the Prophet, Chizkiyahu king of Yehudah, Matityahu ben Yochanan Kohen Gadol Chashmonai, Akavia ben Mahalalel, Rabbi Yochanan ben Zakai, Rabbi Akiva, Rabbi Yiba Saba (mentioned in Zohar Mishpatim), Abaye and others... (Shaar HaGilgulim, hakdamah 36).
Nadav and Avihu were handsome youths (Targum Yonatan, Shemot 24:11).
They did not have wives [because] they were arrogant. Many women remained unmarried, waiting for them, [but] they said, "Our father's brother [Moses] is a king, our mother's brother [Nachshon] is prince [of his Tribe], our father [Aharon] is Kohen Gadol [high priest], and we are assistants of Kohen Gadol. What women are suitable for us?" (Vayikra Rabbah 20:10).
"And the sons of Aharon, Nadav and Avihu each took his fire pan, placed within it fire and placed incense upon it. And they [thus] offered a "strange" fire before HaShem, one that He did not command of them. And a fire came forth from before HaShem and devoured them and they died before HaShem."
It appears evident that God struck down Nadav and Avihu because they committed the sin of "offering a strange fire before God." It is the nature of this "strange fire" that brings up some very important questions.
The sages give many reasons for what happened to these two sons of Aharon. The well-known reasons for their punishment include:
According to pshat, Rabbeynu Bachya, in his commentary of this episode states that the "strange fire" is rather evident. Nadav and Avihu were supposed to ignite the incense offering using the fire from the altar. Apparantly they used another fire source. This then was the strange fire.
Rabbeynu Bachya then continues to offer a Kabbalistic reason. He states that Nadav and Avihu saw the descent of fire from Heaven upon the altar. They recognized that this fire emanated from the supernal place of Judgement. Their concern was that judgement would pass throughout the camp with devastating effects. They thus ran to offer to incense, which was ordained specifically to appease the forces of judgement. Yet, they made one great error.
Whenever one wishes to avert the supernal forces of judgement, it is not enough that one tries to appease them directly. For who has the power to appease the wrath of God? Rather, one must supplicate and depend upon Divine mercy. What one must do then is to call upon the holy essential Name Havaya (The Tetragramaton) and not attempt to go through other channels. This then was their sin. They did the right thing, but did it in the wrong way. In other words, they had good intentions. They just had bad actions. How God judges in an instant like this is clearly evident.
Nadav and Avihu were not commanded to do anything. Yet, they took the initiative on their own. Nadav and Avihu did what they thought what was right, without first checking with the established authorities of their father Aharon and uncle Moshe. While some might interpret this as a good thing. It is evident that God did not!
The method of their death is interesting to note. Rabeinu Bachya states that two thin threads of fire came forth from the Holy Place, (most likely from the Ark of the Covenant) and entered into their noses, thus removing (i.e., burning) their souls. The implication is that physically nothing had happened to them. Although it states, "a fire came forth from before HaShem and devoured them" there was no evidence of any fire or of anything being burned.
The Yitzchak Isaac of Kamarna in his book Heichal Berecha notes that the souls of Nadav and Avihu left their bodies in a state of union with HaShem and that they ascended above to cling to the Tree of Life. Therefore, although the actions of Nadav and Avihu were incorrect, their intentions were pure. They were punished for their wrong actions here in this world and rewarded for their pure intentions in the world to come.
Nadav and Avihu had no transgression other than this. Wherever their death is mentioned, their sin is mentioned, so that the people should not say, "They had hidden misdeeds for which they died" (Vayikra Rabbah 20:8).
The deaths of Nadav and Avihu were recorded in a few places [in the Torah] to teach that there was sadness in the presence of God about them, for Aharon's sons were beloved [by God] (Bamidbar Rabbah 2:23).
May the merit of the tzaddikim Nadav and Avihu protect us all, Amen.