Do not eat anything detestable. (Deuteronomy 14:3)
If an animal intended for an offering became blemished, rendering it unusable, it may not be eaten. This applies specifically in a case where the animal became blemished through some human action, rather than “just because.” (See Talmud Bechoros 34a.) It is also the case if the sacrifice became disqualified after it was already slaughtered. In these cases, the Torah calls the unfit sacrifice an abomination.
In addition to disqualified offerings, this mitzvah also includes such sacrificial “abominations” as nosar (a sacrifice eaten after its prescribed time limit) and piggul (a sacrifice offered with improper intentions – see Mitzvos #143 and #144, respectively), though its specific referent is the blemished sacrifice.
The reason for this mitzvah is that the animal has been sanctified to God. Even though its use as a sacrifice may have been invalidated, that does not give us license. We must condition ourselves to treat that which is holy with extra reverence. This will reinforce within us the trait of proper respect and deference for the Temple in general and for God in particular.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Bechoros on pages 34a-b. It is codified in the Mishneh Torah in the nineteenth chapter of Hilchos Pesulei HaMekudashim. This mitzvah is #140 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos; it is not listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.