Arachin, Chapter 8, Mishnah 6. This chapter has been working through the laws of cherem, property that a person removes from his own possession by declaring it consecrated. Our mishnah now spells out two points: how a cherem that belongs to the kohanim is handed over, and what happens when a person declares a cherem without saying which kind he means.
A cherem of the kohanim cannot be redeemed
The mishnah begins with the halacha itself: "Charmei kohanim", charamim designated for the kohanim, "ein lahem pidyon", are not subject to any process of redemption. Someone who consecrated an object in this way to the kohanim may not hold on to it, evaluate what it is worth, and pay out that sum instead. "Ela nitanim lakohen kitruma": the object itself enters the kohen's possession, on the model of teruma.
The comparison to teruma is the source of the law. When a person separates teruma from his produce, he cannot hold on to the teruma and pay the kohen its worth; the kohen receives the teruma itself. The pesukim teach that a cherem of the kohanim works the same way. The item that was declared cherem passes into the kohen's hands, and money is no substitute for it.
When the person did not specify
Normally the person making such a declaration states where his cherem is headed: either the kohanim are to receive it, or it is dedicated to Hekdesh for bedek habayit, the fund that maintains the structure of the Beit Hamikdash. But what if he pronounced the word "cherem" and added nothing further? On this the Tannaim divide.
"Rabbi Yehuda ben Beteira omer": in his view, "setam charamim lebedek habayit", a cherem declared with no further detail is dedicated to the maintenance fund of Hekdesh. He learns this from the pasuk that calls each cherem "kodesh kadashim hu l'Adonai", holy of holies to Hashem. Since the Torah places cherem in Hashem's domain, a declaration left open belongs to Hashem's own account.
"Vachachamim omrim: setam charamim lakohanim", the Chachamim disagree and rule that an unspecified cherem goes to the kohanim. Their source is the pasuk that speaks of an ancestral field that was consecrated and never redeemed by its owner: "Kisdeh hacherem lakohen tihiyeh achuzato", like a cherem field, his holding shall belong to the kohen. The Torah is comparing that field to the ordinary cherem field, and the comparison only works if the plain, unqualified cherem field is one that belongs to kohanim.
How the Chachamim read the other pasuk
The mishnah now presses the Chachamim with the natural objection: "Im kein, lama ne'emar", if that is so, why does the Torah declare that each cherem is "kodesh kadashim hu l'Adonai"? Should a cherem with no stated destination land in the hands of the kohanim, what is left for the verse cited by Rabbi Yehuda ben Beteira to teach?
Their response: the pasuk comes to teach "shehu chal", that such a declaration takes hold, even with respect to animals that were already consecrated as korbanot, both those classed as kodshei kadashim and those classed as kodashim kalim. That is a real chiddush. The general principle is that no one can consecrate as cherem what is not entirely his own, and a beast already earmarked for the altar has left his full ownership. Nevertheless the Torah rules that korbanot are excluded from that principle: even an animal of the highest grade of sanctity can be made cherem by its owner, and his words are effective.
An animal set aside as a korban is already sanctified and holy, so what it means for a cherem to "take effect" on it needs explaining. That is precisely what the next mishnah will lay out.