The third Mishnah in chapter 8 of Tractate Terumos seems, at first glance, to deal with a subject that is not our concern here, and it would appear to belong to Tractate Ma'asros, which follows it. Tractate Ma'asros deals with the question of when the obligation to tithe food takes effect, and this refers not only to Terumah Gedolah, which is the first separation, but also to Ma'aser Rishon and the like.
The rule governing the obligation to tithe:
As long as food has not reached the stage at which it becomes obligated in tithes, one may eat from it in a casual manner - an incidental, informal eating - as opposed to a fixed eating, which is regular and formal. The threshold from which one must tithe before eating, even casually, is the produce reaching gemar melachah, that is, the completion of its processing. Under normal circumstances this is the stage at which no work remains to be done and the produce is ready for storage.
With grapes, which are the subject of our Mishnah, it is not the way of the world to eat them as they are: a vineyard is generally intended for producing wine, and therefore one who eats fresh grapes is eating from fruit that has not yet reached gemar melachah. Even so, if a person grew the grapes in order to eat them as fruit and not in order to make wine from them, the completion of the harvest from the vines is considered gemar melachah.
However, regarding the obligation to separate tithes, gemar melachah alone is not enough. If a person intends to bring the produce into his home, as opposed to selling it in the marketplace, there is no obligation to tithe until he brings it home, and until then he may eat from it casually. So there are two matters here: gemar melachah, and after it, bringing the produce home.
Nonetheless, there are situations in which, even though the produce has not yet been brought into the house, the Sages required tithing before eating and cancelled the allowance for casual eating. One of these is bringing the fruit into the courtyard.
The status of the courtyard:
In the time of the Mishnah, eating in public was considered improper and undignified, and people ate in private. There is the well known ruling that one who eats in the marketplace is like a dog, and such eating was considered coarse behavior (similar to acts that in our day are considered coarse when done in public). To take a grape and taste it in the marketplace is not objectionable, but to eat a full meal in public was considered entirely undignified, and about this the Sages said that one who does so is like a dog.
A nice aside: Rabbi Victor Miller once saw one of the congregants of his shul eating in public, and said to him: "Don't you know that one who eats in the marketplace is like a dog?" The man answered him: "Rebbe, but that applies specifically to a meal, when one washes his hands and eats bread, whereas this is only a light snack." The Rabbi said to him: "If so, you are not a dog - you are a puppy."
In the view of the Sages, the proper place for eating is the privacy or semi-privacy of the home. The courtyard was a semi-private area: in the time of the Mishnah people lived in something like closed alleyways, in which the houses surrounded a shared area called a courtyard, similar to the lobby of an apartment building today - a private space shared by the residents. The houses were very small, and therefore many activities were carried out in the courtyard: cooking, productive work, and leisure time. Even so, the courtyard remained semi-private, since it was not used by outsiders but only by the members of the courtyard.
Therefore the Sages viewed eating in the courtyard, after fruit whose processing was completed had been brought into it, as eating that requires tithing under normal circumstances, since this is no longer casual eating but eating that has become fixed on account of the produce having been brought home. It is a question whether bringing the produce home is the final stage of gemar melachah, or whether these are two separate matters: gemar melachah in the field and on the agricultural land, and bringing it home as a matter unto itself. Either way, it is clear that one who brings his fruit into his courtyard must tithe it.
The first case: from the garden to the courtyard:
The Mishnah discusses a person who took a cluster of grapes and began eating from it as he walked. Since he was eating in the garden, his eating certainly began as a casual snack, which is exempt from tithing, and there was seemingly no completion of the work either, since we are dealing with grapes and not wine. But now he enters his courtyard, and under ordinary circumstances bringing produce into a courtyard obligates one to tithe. The question, then, is this: someone who began eating casually and happened to pass through the courtyard - must he tithe before continuing to eat, or may he continue, since he began a full-fledged casual eating out in the field?
In the words of the Mishnah: "Hayah ochel ba'eshkol venichnas min haginah lechatzer" - he was eating from a cluster and entered from the garden into the courtyard, that is, he came in from the garden outside to the courtyard, which is semi-private. May he continue eating?
Rabbi Eliezer says: "Yigmor" - he may finish, meaning he may continue eating. This does not mean that he may eat inside the courtyard, for once he has brought the produce into the courtyard he may not eat there without tithing; rather, it means that he may leave the courtyard and resume his casual eating out in the garden.
Rabbi Yehoshua says: "Lo yigmor" - he may not. Once he has brought the produce into the courtyard there is no way back: he is like someone who has formally declared the crop brought home, and therefore he must tithe before he resumes eating. And the halachah follows Rabbi Yehoshua.
The second case: Shabbos took effect upon him:
The second case is very similar: here too he began eating the grapes in the garden in a casual manner, and such eating is permitted, but instead of bringing them into a courtyard something else occurred. In all there are six things that "fix" produce for tithing - things that, although they do not involve bringing the produce home, constitute the crossing of a threshold that obligates tithing:
Bringing produce into a courtyard - as explained above.
Shabbos - one who eats on Shabbos never eats casually. Shabbos is a purpose and a point of completion, everything on it is done in a formal manner, and any eating on Shabbos is considered a fixed meal.
Cooking - a person does not cook his food and then claim that his eating is casual, for by cooking it he has fixed it as a meal.
Beginning to tithe - one who begins the tithing process must complete it, and cannot stop in the middle.
Pickling - one who pickles his produce, cucumbers for example, can no longer say that his eating is casual, since by pickling he has, to a certain degree, fixed it as a meal.
Our case, then, is this: he began eating the grapes on Erev Shabbos and Shabbos arrived. Must he now tithe in order to continue eating? Here it is worth noting in advance that the Mishnah is somewhat tangled, because there are two versions that contradict one another: the dispute is between Rabbi Eliezer and Rabbi Yehoshua, but there are texts that attribute each position to the other Tanna, so that in some the first opinion is Rabbi Yehoshua and in others the first opinion is Rabbi Eliezer. We will present the version before us, and in any event the halachah follows Rabbi Yehoshua, since the halachah always follows him against Rabbi Eliezer - but in practice the halachah depends on which version we have.
In the words of the Mishnah: "Cheshchah leilei Shabbos" - night fell on Friday evening: he was eating his grapes on Erev Shabbos, the sun set and Shabbos night arrived. May he continue eating from those same grapes?
Rabbi Eliezer says: "Yigmor" - he may finish the grapes. This does not mean that he may eat them on Shabbos without tithing, for all eating on Shabbos is considered fixed and is forbidden; rather, it means that after Shabbos ends, since he began eating from the cluster beforehand, he may go back and eat from that very same cluster without tithing it. On Shabbos itself he may not eat them, since it is also impossible to tithe on Shabbos, because doing so looks like repairing, for he is in fact repairing the fruit - a rabbinic offshoot of the melachah of makeh bepatish.
Rabbi Yehoshua says: "Lo yigmor" - he may not eat any more from this cluster, even after Shabbos ends, until he tithes. On Shabbos itself it is obvious that he does not eat them, since they are untithed, and even afterward he does not eat them, because Shabbos fixed them and also brought them across the absolute finish line that obligates tithing.
And the halachah follows Rabbi Yehoshua. But as noted, what Rabbi Yehoshua's position actually is - that itself is subject to dispute, that is, to the difference between the various versions of the Mishnah.