This is what's due to the Kohanim (priests) from the people. Whoever slaughters an animal, whether it's a sheep or a goat, gives the Kohen the foreleg, the jaw, and the stomach. When a person slaughters an animal from his cattle, sheep, or goats, he has to give three different parts of the animal to the Kohen: the foreleg, which is the right foreleg; the jaw; and the stomach. There are four different stomachs. The fourth stomach of the animal is where it chews its cud. These all have to go to the Kohen. They're part of the matanot, gifts, which go to the Kohanim.
The Mishnah says that giving the foreleg, the jaw, and the stomach applies to animals both in Eretz Yisrael and outside of Eretz Yisrael, whether the Beit HaMikdash is around, was destroyed, or did not exist. It applies to unconsecrated animals, regular animals that are being used for food, but not for mukdashim, not for consecrated animals. The following logic should apply to tell us that consecrated animals, korbanot (offerings), should be included in these matanot as well.
With unconsecrated animals, Chullin, we are lenient in that we do not have to give the breast and the thigh to the Kohanim. But still, we are chayavin b'matanot (obligated in gifts). But still, we give the matanot, the leg, the jaws, and the stomach. Kodashim, consecrated animals, specifically Kodashim Kalim (lesser sanctities). But with Kodashim, we do give the Chazeh VeShok (breast and thigh). But Kodashim, shechayavin b'Chazeh VeShok, consecrated animals that we treat strictly and for which we do have to give the breast and the thigh to the Kohen—Eino Din, shechayavin b'Chazeh VeShok: shouldn't logic dictate that we should also give the matanot, sort of a Kal VaChomer (a fortiori argument)?
If we're giving the matanot, sort of a Kal VaChomer—the Chazeh VeShok by the Kodashim, by the Kodashim Kalim—shouldn't we? And we don't have to give it here, in the unconsecrated animals. So, isn't it a Kal VaChomer? So if we're giving it on the unconsecrated animals—the matanot—shouldn't we also have to give it in the Kodashim Kalim?
Talmud lomar: the Torah tells us regarding the thigh and the breast of consecrated animals, “Va'eten otam le'Aharon haKohen ul'vanav lechok olam”—“I have given them to Aharon and his children as an everlasting right.” Ein lo ela mah she'amur ba'inyan: the fact here that it says it's only to them. Va'eten otam, the word otam implies that Aharon has a right only to what's mentioned in that pasuk (verse), which is the Chazeh VeShok, the thigh and the breast.
But the other gifts, the foreleg, the jaws, and the stomach, are not applicable in that context. So, in other words, we're limiting what you could learn from here. The owner of the korban is only obligated to give the breast and the thigh to the Kohen, but not the leg, the jaws, and the stomach. So that's where we limit what we learn from here. We say that what's given to him is only specifically what's mentioned in the pasuk. Therefore, with korbanot, he only gets the Chazeh VeShok. When we're talking about Chullin, unconsecrated animals, the foreleg, the jaws, and the stomach also apply there. So there are two separate obligations of what has to be given to the Kohen.