Welcome to Maseches Shevi'is, which deals with the laws of shemittah - laws that are practically relevant this year in Eretz Yisrael. We begin with Chapter 1, Mishnah 1, where the Mishnah opens its discussion of 'tosefes shevi'is': the halachah that requires us to add onto the shemittah year a period of time during which it is forbidden to perform in the field the labors prohibited during the seventh year. In other words, the shemittah prohibitions are extended backward into the sixth year.
How long is this addition?
From the Torah: It is a halachah l'Moshe miSinai to add thirty days before Rosh Hashanah, during which one may not perform these labors in the field.
From the Rabbanan: The Sages extended the period even further, and in their enactment they distinguished between an orchard (a field of trees) and a grain field, where produce such as wheat grows.
The law of the orchard in our Mishnah:
The Mishnah first discusses the law of an orchard: until when may one plow - plowing being one of the labors forbidden during the seventh year - in a field of trees on the eve of shemittah?
Beis Shammai say: As long as the plowing benefits the fruit presently on the tree, since then it is clear that it is being done for the needs of the sixth year and not for the needs of the seventh.
Beis Hillel say: "Ad Shavuos" - until Shavuos; that is the time that was fixed.
And the Mishnah concludes: "Kerovin divrei eilu lihyos k'divrei eilu" - the words of these are close to the words of these; although Beis Shammai and Beis Hillel used different formulations, in practice they refer to nearly the same point in time. And as far as the halachah is concerned, we of course follow the words of Beis Hillel.
The first Mishnah and its annulment:
Everything said until now refers to what is called the 'first Mishnah' - the original way in which this halachah was established. However, after the era of this Mishnah, Rabban Gamliel and his beis din annulled the law of tosefes shevi'is, since shemittah nowadays is only rabbinic, and they therefore ruled that there is no need to observe tosefes shevi'is at all.
In summary: Our Mishnah represents the 'first Mishnah,' according to which the addition was not limited to the thirty days before Rosh Hashanah derived from halachah l'Moshe miSinai, but rather began earlier than that - until Shavuos, according to Beis Hillel - in the case of an orchard.
In the next section we will see that for a grain field, for wheat and the like, a different time was set: until Pesach.