Anyone who eats from it will bear his sin… (Leviticus 19:8)
Sacrifices have time limits during which they must be eaten. Anything that remains of them past their designated times is called nosar – “left over” – and may no longer be eaten.
In Mitzvah #144, we discussed piggul – a sacrifice rendered “detestable” by having been offered with improper intentions. Even though the intention to eat a sacrifice after its time has expired is one of these invalidating intentions, the prohibition against planning to do so and that against actually doing so are two separate mitzvos. Both mitzvos may be derived from Exodus 29:34, but each has its own verse expressing its punishment (Leviticus 7:18 and here, respectively). The Talmud in Me’ilah (17b) says that the nosar and piggul are two distinct mitzvos, though they are closely related and the Talmud does extrapolate laws from one and apply them to the other.
The rationale underlying this mitzvah is similar to that of piggul: sacrifices are intended to draw us closer to God. He instructed us in the proper procedures of how to accomplish this. For us to second-guess Him and act otherwise flies in the face of why we offer sacrifices in the first place. (As far as why God would impose a time limit on sacrifices to begin with, the nature of meat is to go bad. After a couple of days, it’s not looking so good. To eat such a thing that’s clearly “on the way out” would no longer bring honor to the Temple service.)
This mitzvah applied to both men and women in Temple times. It is discussed in the Talmud in the Order of Kodshim, particularly in the tractates of Me’ilah (17b) and Zevachim (56b). It is codified in the Mishneh Torah in the eighteenth chapter of Hilchos Pesulei HaMukdashin and is #131 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.