The offerings are a means of communicating with Hashem, and each offering has its own meaning and regulations. Some offerings are completely incinerated on the Altar, while others have certain parts that are eaten either by the Kohanim or the owners. The Torah sets a time limit for the consumption of these parts, after which any remaining meat becomes classified as "nosar" (leftover). This meat must be burned and cannot be consumed, but the offering itself remains valid. If an animal is offered with the intention of eating it after the designated time limit, it is called "pigul" (repulsive). Not only does the meat become prohibited, but the entire offering becomes invalidated.

Hashem commands us with these mitzvos so that we will treat the service in the Beis HaMikdash with the utmost respect. Meat starts to rot over time, so we must eat it before that happens, hence the time limit. If the time limit passes, we must burn it so that the sacred meat does not undergo the disgrace of being a cause of disgust (Chinuch). Because of the great respect due to the offerings, even the mere thought of eating them outside their timeframes suffices to invalidate them (Moreh Nevuchim).

Another reason why the Torah attaches great importance to the intention at the time of the service is that this is the offering’s primary element, as the Sages say, “Hashem desires the heart.” Thus, we find that when the Beis HaMikdash was destroyed and the offerings ceased, the Sages enacted for us to communicate to Hashem the intentions of our hearts through prayers, as a partial substitute for the offerings. Therefore, even if the offering is physically perfect and the service is performed flawlessly, a corrupt intention can invalidate it entirely (Ralbag, Chinuch, and Rav Menachem HaBavli). Due to the great sacredness of the otherwise valid offering, one who intentionally eats it in a defiled state of pigul is punished with spiritual excision (Emes L’Yaakov; see also Rav Hirsch).

On a deeper level, when an offering is brought, a Divine light shines throughout the day of the service, imbuing the offering with sanctity. When that sanctity departs the following day, that Divine light departs from the offering, leaving a void of holiness. Forces of impurity converge to fill that void, just as they attach themselves to a dead body that has become emptied of its soul. Even the intention to eat an offering after its set time can cause a similar negative spiritual effect to the offering, and its consumption is therefore prohibited (Recaniti to Vayikra 7:15 and Ramchal, Sharashei HaMitzvos §29).