Menachos Chapter 10, Mishnah 9 - the final mishnah of the chapter and the last one dealing with the Omer offering. The mishnah continues to list the times and circumstances in which one is permitted to harvest grain before the barley for the Omer meal offering is cut, and then discusses how the Omer itself is harvested and brought.
The permitted cases of harvesting before the Omer:
"Kotzrim mipnei hanetios" - one may harvest grain that grew among young saplings. This grain is, as it were, in competition with the young trees, and cutting it is comparable to weeding: it is removed so that the nutrients will reach the trees directly and not be diverted to it. Since it grew among the trees, it does not receive full nourishment and is not fit to be used for the barley of the Omer in the first place, and therefore there is no rabbinic prohibition against cutting it. All that remains is the rabbinic restriction against mixing it in, as the mishnah goes on to explain.
"Mipnei beis ha'avel" - in the time of the mishnah the practice was that after the mourners returned from the burial a meal of consolation was held, a sort of large communal meal with friends and family. Such a meal requires a spacious area, larger than a private home can hold, and so it was generally held outdoors. If the only available space is in the fields, and it needs to be cleared, one may harvest and remove the grain growing there so that there will be room to sit and comfort the mourners. The basis for this permission, even though the grain in question is fit for the Omer, lies in the wording of the verse "reishis ketzirchem" - a harvest that is for your own needs. One who harvests not for his own personal use but for the sake of a mitzvah, to prepare the place for the mourners, is acting permissibly.
"Mipnei bitul beis hamidrash" - in order to accommodate those who otherwise could not learn in the beis midrash. When the beis midrash is full and there is no room to seat the students, who were accustomed to sit and learn on the floor, a place is prepared for them outdoors. And if the only available outdoor space needs to be cleared of the grain growing there, one may harvest it in order to make Torah study possible.
It is worth noting that the Bartenura's version of the text reads "mipnei beis hamidrash" - so that there will be a place to learn. The idea is the same, only the wording of the text differs.
How this permitted harvesting is done:
Regarding these permitted harvests the mishnah says: "Lo ya'aseh osan kerichos, aval manichan tzevasim" - one may not tie the stalks into bundles at the time of harvesting; rather, the cut stalks are left lying on the ground and are bound only after the Omer has been offered. The idea is not to add labor, and to make clear that this harvesting is being done by special dispensation and in an unusual manner, yet it remains limited, and one certainly may not eat from the grain. Some explain that "kerichos" are large tied bundles and "tzevasim" are small ones; in any event, the harvesting and binding are done in an unusual way.
The ideal and the acceptable in bringing the Omer:
"Mitzvah lavo min hakamah" - ideally the barley for the Omer meal offering should be brought from standing grain, that is, from grain still attached to the ground. The source for this is the verse in Devarim, in Parashas Re'eh, in the context of counting the Omer: "meihachel chermesh bakamah" - from the time the sickle touches the standing grain. And if "lo matza" - he did not find standing barley fit for use, for whatever reason - "yavi min ha'omarim", he brings from grain that was already cut from the ground earlier, before the sixteenth of Nissan.
"Mitzvah lavo min halach" - ideally from moist kernels, as the verse says, "karmel." The Gemara brings two expositions of the word's meaning, and Rashi and Onkelos each adopt one of them: "kar malei," like a full cushion, or "rach umal," soft and easily crushed. In other words, ideally the grain should be full and moist. And if he did not find moist grain, he brings from dry grain, and even dry barley is acceptable after the fact.
"Mitzvah liktzor balaylah" - ideally the barley should be harvested on the night following the first day of Pesach, the night of the sixteenth of Nissan, for the verse says "sheva Shabbasos temimos," complete weeks, and therefore one should harvest as close as possible to the beginning of the seven weeks. And if it was harvested by day, it is acceptable after the fact.
What is the source that even the less-than-ideal option is acceptable? In the passage about the Omer it says: "And if you bring a meal offering of first fruits to Hashem, fresh grain roasted over fire, coarsely ground kernels, shall you bring as the meal offering of your first fruits" - the grain must be fresh, roasted over fire, coarsely ground ("geres"), and full of kernels ("karmel"). The word "takriv" ("shall you bring") is repeated in the same verse, and this repetition seems superfluous. From here the Sages derived that there are two kinds of offering: an ideal offering and an after-the-fact offering. Therefore, even when a person is unable to bring it in the perfect manner, he brings it in the after-the-fact manner.
It is worth noting that the question of when the harvesting takes place is a dispute among the Tannaim, brought in Maseches Megillah, chapter two. Our mishnah follows the view of Rabbi, that is, Rabbi Yehudah HaNasi, who holds that it may be harvested even by day; Rabbi Elazar ben Shimon, in contrast, holds that the harvesting must be done specifically at night.
"Vedocheh es haShabbos":
What is it that overrides Shabbos here? It does not mean that the harvesting itself is done on Shabbos, even though that is the halachah in practice. The view of the Tanna before us is that the harvesting may be done at any time, by day or by night, and therefore it need not override Shabbos. The correct reading of the mishnah, then, is that the offering of the Omer meal offering overrides Shabbos, and not the harvesting, which is not fixed to a particular time and can be done before Shabbos.
Nevertheless, the halachah was decided in accordance with the Tanna whose view we have followed throughout the entire chapter: both the reaping and the offering of the Omer meal offering override Shabbos, and that is the law in practice. With this the tenth chapter is complete, and with it the subject of the Omer offering.