Chagigah, Chapter 3, Mishnah 7. At the end of the previous mishnah we learned that during the festival, throughout the days of the holiday, all the amei ha'aretz were considered chaverim, and they were believed regarding tumah and taharah even with respect to Terumah. This trustworthiness, however, applied only during the festival itself; once the festival passed, they are no longer believed. This raises a question: what is the status of items that were opened and that amei ha'aretz touched during the festival, once the festival has ended?
"Hapotei'ach es chavito v'hamaschil b'isaso al gav haregel":
The mishnah deals with someone who opened a barrel in order to sell wine in Jerusalem, and because of the festival amei ha'aretz touched it, and likewise with someone who began preparing his dough because of the festival and amei ha'aretz touched it. During the festival they are believed, and everything is considered tahor. The question is what the status of the remainder is - the wine left in the barrel and the dough left over - once the festival has passed.
Rabbi Yehudah says: "Yigmor" - he may finish and maintain the remainder in its state of purity even after the festival. The Gemara explains the reason: if we did not permit him to finish and to treat the item as tahor after the festival, no one would be willing to begin at all, and this would cause a shortage of supplies for the pilgrims who came to Jerusalem to stay there for the festival.
"V'chachamim omrim: lo yigmor" - the Sages disagree with Rabbi Yehudah and hold that once the festival has passed, we no longer maintain the remainder in a presumption of purity.
Purifying the Azarah after the festival:
The mishnah continues with a historical fact and a practical directive in the Beis HaMikdash: "Mishe'avar haregel hayu ma'avirin al taharas ha'azarah" - they would remove the vessels of the Temple from their place in order to immerse them in a mikvah. The reason: amei ha'aretz had touched the vessels during the festival, and during the festival that presented no problem; but once the festival passed, the vessels are considered tamei retroactively, and therefore they must be immersed in a mikvah and purified.
When was this process of "ma'avirin al taharas ha'azarah" carried out?
"Avar haregel b'yom shishi - lo hayu ma'avirin mipnei kevod haShabbos": when the last day of the festival fell on Thursday and isru chag fell on Friday, they would not perform the purification of the Azarah on Friday out of respect for Shabbos, since the kohanim were occupied with preparations for Shabbos and with the needs of their households, and therefore they postponed the purification of the vessels until after Shabbos.
Rabbi Yehudah says: even when the last day of the festival fell on Wednesday and isru chag fell on Thursday, they would not perform the purification, because even then the kohanim were not free: they were busy removing the ash that had accumulated on the altar, a task that took time; and on Friday they were once again occupied with preparations for Shabbos. It emerges that the purification of the vessels was postponed until after Shabbos ended.
In summary: in this mishnah we learned the law of one who opens his barrel and begins his dough because of the festival - whether he may finish and maintain the remainder in purity even after the festival (Rabbi Yehudah) or not (the Sages), and also the procedure for purifying the Azarah after the festival: immersing the vessels that amei ha'aretz had touched, and postponing the purification out of respect for Shabbos and because the kohanim were occupied with removing the ash from the altar.