News From Ramaz
By Ezra A. (Grade 6)
The Torah introduces the service of Yom Kippur by saying that God spoke to Moshe after the death of Aharon's two sons Nadav and Avihu. This means that there is a connection between this tragedy and the Yom Kippur service. In addition, the pasuk adds a new dimension to the cause of their death by saying that they died when they approached before Hashem. This element was omitted from the parasha in perek י pasukim א-ב which mentioned only their sin of offering an unbidden incense or fire as cause for their deaths. From the description here, however, it would seem that they were punished only for entering an area that was forbidden to them, which was the modest Kodesh Hakodashim. The only time the Kohen Gadol can go in there is on Yom Kippur.
Another answer is that because just as Yom Kippur brings atonement so does the death of a righteous person. Our sages explain that Yom Kippur is Et Ratzon, a time of favor and opportunity for atonement. When a righteous person like Nadav or Avihu dies and his soul ascends to the world of souls, the other righteous souls in heaven rejoice at his coming. This good feeling above can inspire a spirit of forgiveness and atonement to the righteous person's survivors on earth.
These are the connections between the death of Nadav and Avihu and the Yom Kippur service.