After Nadav and Avihu died, Moshe told Aharon to eat the mincha and shelamim brought that day even though he was an onein. Aharon and his sons burned a chatas, Moshe got angry, they gave a cryptic explanation, and Moshe was satisfied.
Coming off of Pesachim 7:9, which discusses when you burn korbanos that become invalid for different reasons, the Gemara discusses various explanations of this story. The most famous ones are the ones quoted by Rashi in Chumash - either it was the chatas of Rosh Chodesh and was burned because nobody could eat it, following one interpretation of R' Yochanan ben Berokah in the mishnah, or it became tamei.
Another explanation in the Gemara is that it was a hora'as sha'ah, a temporary exception to the normal halacha.
Typically, hora'os sha'ah are needed to send a message. Probably the most dramatic example is Eliyahu bringing an offering outside of the Beis Hamikdash on Har Hakarmel. It's obvious why he needed to do that - he had to run his experiment to discredit the Baal's prophets, and they wouldn't have agreed to do it inside the Beis Hamikdash.
Why was an exception needed here? Why, according to Tana devei Rabba bar Avuha, couldn't they just burn it the following day?