Sukkah, Chapter 4, Mishnah 3. In the first Mishnah of the chapter we learned that the taking of the aravah (willow branch) in the Beis HaMikdash was sometimes practiced for six days and sometimes for seven. Our Mishnah comes to spell out in which circumstance each of these rulings applies.
"Aravah shivah keitzad":
The Mishnah asks: in which case was the aravah taken in the Beis HaMikdash all seven days? And it answers: "Yom shevi'i shel aravah shechal lihyos b'Shabbos" - when the seventh day of the aravah falls on Shabbos. The seventh day of taking the aravah is Hoshana Rabbah, and everything depends on it:
Seven days: When the seventh day - Hoshana Rabbah - fell on Shabbos, the aravah was taken on all seven days of the festival, including on Shabbos itself.
Six days: When Shabbos fell on one of the other days of the festival, the aravah was not taken on Shabbos, and it turns out that it was taken for six days only.
The reason for this:
The Gemara explains that this mitzvah is not stated explicitly in the Torah; rather, it is a halachah given to Moshe at Sinai, transmitted through tradition. Therefore, in order to publicize that it is from the Torah, the Sages established that it should override Shabbos. However, they did not want to establish this on the first day, because then it would not have been noticeable - after all, Shabbos is already overridden in any case for the mitzvah of lulav and esrog. In order to show that this is a separate and distinct mitzvah in its own right, they set the overriding of Shabbos on a different day, the final day of the festival.
Nowadays:
Today we take the aravah on the seventh day alone. This is a custom of the prophets, to take it even outside the Beis HaMikdash on Hoshana Rabbah, in order to remember the mitzvah as it was performed in the Beis HaMikdash.
In summary: In this Mishnah we learned that the taking of the aravah in the Beis HaMikdash was practiced for seven days when Hoshana Rabbah fell on Shabbos, and for six days when Shabbos fell on one of the other days of the festival. The reason is that the aravah is a halachah given to Moshe at Sinai, and in order to publicize that it is from the Torah they established that it override Shabbos specifically on the final day, when the mitzvah stands out on its own. And nowadays we take the aravah on Hoshana Rabbah alone, as a custom of the prophets, in memory of the mitzvah performed in the Beis HaMikdash.