That they entered: To do their Avodah.
Whilst inebriated: On the verse reporting their demise RaShi states on the words: And fire went forth: Rabbi Eliezer says: Aharon’s sons died only because they rendered halachic decisions in the presence of Moshe, their teacher. Rabbi Yishmoel says: [They died because] they had entered the sanctuary after having drunk wine. The proof is that after their death, [Scripture] admonished the survivors that they may not enter the sanctuary after having drunk wine. This is analogous to a king who had a faithful attendant. [When he found him standing at tavern entrances, he severed his head in silence and appointed another attendant in his place. We would not know why he put the first to death, but for his enjoining the second thus, “You must not enter the doorway of taverns,” from which we know that for such a reason he had put the first one to death. Thus [it is said], “And fire went forth from before HaShem and consumed them, and they died before HaShem.” But we would not know why they [Nodov and Avihu] died, but for His commanding Aharon, “Do not drink wine that will lead to intoxication.” We know from this that they died precisely on account of the wine. For this reason Scripture showed love to Aaron by directing the Divine utterance to him alone, thus, “Do not drink wine that will lead to intoxication,”] as recounted in Vayikra Rabbah (12:1).
As the Possuk testifies: “I will be sanctified through those near to Me”. From this it is understood that there is something very lofty about them entering in an inebriated state.
The Possuk: Vayikra (10:3) “Then Moshe said to Aharon, "This is what HaShem spoke, [when He said], 'I will be sanctified through those near to Me, and before all the people I will be glorified.' " And Aharon was silent.” The Possuk (Vayikrah 10:1-3) “Aharon's sons, Nodov and Avihu, each took his pan, put fire in them, and placed incense upon it, and they brought before HaShem foreign fire, which He had not commanded them. And fire went forth from before HaShem and consumed them, and they died before HaShem. Then Moshe said to Aharon, "This is what HaShem spoke, [when He said], 'I will be sanctified through those near to Me, and before all the people I will be glorified. Aharon was silent.” RaShi comments (Highlighting the words: ‘This is what HaShem spoke’) and says: But when did He speak? [It was when He said], “And I will meet with the B’nei Yisroel, and it will be sanctified through My glory.” Do not read “through My glory,” but “through My honourable ones.” Moshe said to Aharon, “Aharon, my brother! I knew that this House was to be sanctified through the beloved ones of the Omnipresent, but I thought it would be either through me or through you. Now I see that they [Nodov and Avihu] were greater than I or you!”
