As we said in the previous mitzvah, if a sacrifice became ritually impure, it was forbidden to be eaten. We see here that one is obligated to burn it. The reason is as we have stated above: sacrifices are meant to be held in high esteem and becoming ritually impure is a disgrace to the sacrifice. Furthermore, since it can’t be eaten, what else are we going to do with this meat just lying around? It’s going to spoil and stink, which would be a further disgrace to the sacrifice. And so, we burn it.
As we said regarding nosar (a sacrifice left over past its permitted time – see Mitzvah #143), the fact that we are commanded to burn it rather than using it for some other purpose, such as dog food, teaches us a lesson about putting our trust in God. He told us to burn this meat, so we must rely upon Him. Our limited human intellects may tell us that we have a need for this meat and that it’s wasteful to burn it, but we subjugate our thoughts in deference to His knowledge. So should we do when it comes to all mitzvos!
Sacrifices that became tamei (ritually impure) at the Temple were burned at the Temple, unlike nosar, which was burned at home by the one who brought the sacrifice. The bones were not burned, which the Sefer HaChinuch says reinforces his reasoning about the leftover meat putrefying. (A Passover sacrifice is an exception to the general rule of not burning bones; this is because there’s a special rule not to break the bones of the korban Pesach.)
It was not only impurified meat that had to be burned; the same rule applied to flour offerings.
This mitzvah applied to everyone in Temple times. It is discussed in the Talmud in tractates Pesachim (82a-83a), Temurah (34a) and Shabbos (25a). It is codified in the Mishneh Torah in the nineteenth chapter of Hilchos Pesulei HaMukdashin. It is #90 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.