Parshas Shemini begins with the words Vayehi Beyom HaShemini. We learn that the opening Vayehi, And It Was, portends a mixture of tragedy and joy. As in Vayehi Yaakov, that saw Yaakov reunited and living with his son Yosef but in exile and as a prelude to slavery.
Shemini begins with the final dedication of the Mishkan, on the eight day after seven days of Moshe Rabbeinu performing the Avodah, bringing the Korbanot, Aaron steps into his role as Kohen Gadol, brings the Korbanot and as both brothers leave the Ohel Moed at the conclusions, they are privileged to see the Shekihna appear. A heavenly fire consumes the Korbanot. But Vayhei, though there is celebration there is also tragedy.
Two of Aaron's sons bring an alien fire and are killed by fire from heaven. Moshe tells Aaron that with this event the word of G-d, Bekrovai Ekodesh, has been fulfilled. Moshe warns his brother and the remaining sons not to leave, not to mourn and to eat of the Mincha. Aaron and his sons do all this and eat of the Mincha but the Seir brought for Rosh Chodesh, they burn entirely and Moshe demands an explanation.
Aaron's answer however is enigmatic, indicating that he had acted properly and seems to fully satisfy his brother. Yet is short on detail. The two most common explanations are that either the animal became posul or that only Kodshei Shaa like the Mincha were to be eaten, while Onenim, but not Kodshei Dorot. Yet this too leaves something out.
It's notable that the Pasuk appears to be engaging in a virtual pun, as Aaron and his two remaining sons, NaNotrim, are told to eat the Mincha, HaNotrot. Both Aaron's surviving sons and the Mincha seems to be described with the same term. But obviously it's not mere wordplay, there is a message and a point to it.
The Mincha that they are to eat is the remaining Mincha that had not been burnt, just as the two surviving sons, were the remaining sons who had not been burnt. Moshe describes the deaths of Nadav and Avihu, not as punishment but as glorification, much like a Korban. Like the Mincha, part had been burnt and part remained for Aaron. When Moshe warns them about leaving with the oil on them, as there is oil on the Mincha, the implication is that they too will die. This is what is done with a Korban that becomes Posul, to be burnt outside. So if they leave, they too will be burned outside and what has been a Mincha will become an entirely Posul Korban, which could altogether invalidate the entire Miluim.
Aaron and his sons eat the Mincha and the Korbanot which are Kodshei Shaa. Even though the sons are regular Kohanim and Onenim. But they are Onenim over the deaths of Nadav and Avihu and Nadav and Avihu were themselves a Kodshei Shaa Korban, so to speak, a one time event. Both those deaths and the special status of Elazar and Yithamar were unique events, Shaa. By contrast the Seir of Rosh Chodesh was a Kodshei Dorot and as far as the Dorot were to be concerned, Kohanim Onenim could not consume Kodshim. The holiness of the hour had been gained at great cost, like the reunion of Yosef and Yaakov, a terrible price had been paid. But it was a temporary price. The achievement that had been gained however was one for generations.