The Mishnah deals with someone who pickles three different kinds of vegetables together in one barrel. Each of the three kinds has its own time of biur (removal), since the time of biur for any given kind depends on when that kind is finished from the field. The question, then, is what the status of vegetables pickled together in a single barrel is.
Three approaches to this question:
Rabbi Eliezer: All three kinds are eaten according to the first of them, the one that is finished from the field earliest. Once the time of biur has arrived for the first kind, the others may not be eaten either, because the taste of the kind that became obligated in biur has been absorbed into the other kinds. This follows the rule for all forbidden foods: once the taste of a forbidden item is found in other items, those items may no longer be eaten.
Rabbi Yehoshua: They are eaten according to the last of the kinds. The very fact that one of the kinds in the barrel has not yet been finished from the field permits the other two, since the taste of the kind that is still available in the field makes all the pickled vegetables as though their time of biur has not yet arrived.
Rabban Gamliel: Each vegetable is judged on its own. Once a particular kind is finished from the field, that kind must be removed from the barrel, and the other kinds remain permitted.
The halachic ruling:
The Mishnah rules that the halachah follows Rabban Gamliel. The Rambam, in his Commentary on the Mishnah, points out an interesting detail: the halachah is indeed like Rabban Gamliel, but we do not rule that way simply because the Mishnah says so, for we do not decide halachah on the basis of what is written in a mishnah. The reason is that Rabban Gamliel's view is identical to the view of Rabbi, and the halachah is that we rule like Rabbi against the one who disagrees with him. So the ordinary halachic reasoning leads to the very same conclusion.
Rabbi Shimon's approach:
Rabbi Shimon says: "Kol yarak echad la'biur" - all vegetables have one law with regard to biur, and they are all considered a single kind. Therefore, as long as any vegetable at all still exists in the field, that is enough to allow one to continue eating the vegetables in the house.
The law of regilah:
The Mishnah continues with the law of a particular kind of vegetable, and these are not the words of Rabbi Shimon but of the first tanna: "Ochlin ba'regilah ad she'yichlu sigariyos mi'bik'as Beis Netofah" - regilah is a kind of vegetable (some identify it with purslane), and sigariyos are a variety of regilah that grows in the valley of Beis Netofah. As long as the sigariyos in the valley of Beis Netofah actually still exist, regilah may be eaten, and once they are finished, the regilah in the house may no longer be eaten.
In summary: Regarding three kinds of vegetables pickled in one barrel, the Tannaim disagree: Rabbi Eliezer forbids them all once the first is finished, because its taste is mixed into the others; Rabbi Yehoshua permits them all as long as the last one has not been finished; and Rabban Gamliel judges each kind on its own - and that is the halachah, because his view matches the view of Rabbi. Rabbi Shimon holds that all vegetables are one kind with regard to biur. And as for regilah, eating it depends on the sigariyos in the valley of Beis Netofah.