Tevul Yom, Chapter 4, Mishnah 3. Until now the tractate has been occupied largely with people who carry the status of tevul yom. Here the Mishnah turns to a vessel that carries the very same status, and asks whether dough may be prepared in it and challah taken from that dough.
A word of background. Someone or something that has contracted tumah and has then been immersed in a mikveh is not yet fully tahor. The immersion has begun the process, but the taharah is completed only with nightfall. Throughout that interval, from the immersion until the sun sets, the person or the utensil is called a tevul yom: literally, one who immersed today and is still waiting for the day to end. A tevul yom is no longer tamei in the full sense, yet it is not yet clean either, and whatever it touches is left with a weakened, third degree of tumah, a shlishi.
Now to the situation the Mishnah sets before us: "Areivah shehi tevulas yom." An areivah is the large trough in which dough is worked by hand. This one had picked up tumah at some earlier point, and it was afterward dipped in a mikveh; the sun, however, has not yet gone down, so the vessel remains in that in-between state, its taharah awaiting the arrival of night.
What may be done with such a bowl? "Loshin bah es ha'isa", dough may be kneaded in it. "Vekotzin mimena challah", and a portion may then be cut off from that dough to serve as challah. "Makefes vekorin lah shem", the piece is brought close and is then designated aloud by name as challah.
And why should all this be permitted? The Mishnah answers in three words: "mipnei shehi shlishi." Whatever the vessel passed along to the dough amounts to no more than a third remove of tumah. Then comes the rule that settles the matter: "vehashlishi tahor lechullin." Where the food at hand is chullin, everyday food carrying no sanctity, a shlishi is reckoned as clean outright. While it lies in the trough, this dough is nothing but plain unconsecrated dough, and a tumah of the third remove gets no grip on it at all.
The lesson of the Mishnah, then, is the limited reach of the tevul yom. Its touch does not carry tumah far enough to matter for ordinary food, and so an entire batch of dough may be kneaded in a trough that is still waiting for sunset, the challah portion cut from it, brought near, and named, all without any concern.