In the previous Mishnah, we said that a Kohen (priest) who has no share in the meat of the Olah (burnt offering) also has no share in the skins. Now we'll talk about other rules governing when the Kohen does or does not get the skins.
The Mishnah says: If the Mizbeach (altar) has not acquired the meat, even for a moment—in other words, if the Olah became invalid before the blood was thrown onto the Mizbeach—the Kohanim do not acquire these skins. How do we learn this? The Pasuk (verse) tells us that the Kohen receives the hide or skins of a man's Olah offering. So we say that only if the Olah counted for a man, if the offering became invalid before the blood was thrown, it does not count for the man. The Kohanim do not get the skins either.
But an Olah offering that was slaughtered not for its own sake, but for the sake of a different korban (offering), was done inappropriately. Even though it does not count for the owner toward the fulfillment of his obligation, you have to have proper thoughts in mind in order for it to count for its owner, for his obligations. We still say that the hide—the skins—do go to the Kohanim, because the offering, the korban that was given, was an Olat Ish. It was the Olah of a certain man, in a certain respect. “Echad Olat Ha'ish, Ve'echad Olat Ha'isha, Oroteihen LaKohanim”: whether the Olah was that of a man, or if the Olah was that of a woman, the skins go to the Kohanim. The fact that we call it Olat Ha'ish in the context of giving over the skins to the Kohanim doesn't literally mean only a man's Olah; rather, it's also a woman's Olah.