Mishnah 4 in the second chapter of Maseches Avodah Zarah brings three disputes between Rabbi Meir and the Sages, and all of them revolve around a single question: is the item forbidden in benefit - meaning that one may not even derive financial gain from it - or is it forbidden only in eating, so that its owner may sell it to someone else? Let us go through them one at a time.
The first dispute - gentile wineskins and jugs:
The Mishnah opens with "nodos ha'ovdei kochavim v'kankeneihem" - the wineskins of gentiles and their jugs. A nod is a leather skin, the hide of a sheep or a goat that was turned inside out and adapted for storing wine; a kankan is an earthenware vessel. Both vessels are used to hold wine, and when a gentile used them, the wine inside is yayin nesech, or at the very least stam yeinam, and is forbidden in benefit.
The Mishnah is discussing a case where the vessel was emptied and cleaned, "v'yayin shel Yisrael kanus bahen" - and afterwards a Jew's kosher wine was placed inside it. The question is whether we must be concerned about the taste absorbed into the walls of the vessel, which now seeps out into the kosher wine. Rabbi Meir is stringent: "asurin, v'issuran issur hana'ah - divrei Rabbi Meir" - they are forbidden, and their prohibition is a prohibition of benefit; whereas "Chachamim omrim: ein issuran issur hana'ah" - the Sages say that their prohibition is not a prohibition of benefit. There is only a prohibition of drinking, and one may sell the wine and derive financial gain from it.
The point of the dispute: the well known rule, which we will yet see later in the tractate, is that yayin nesech that became mixed into kosher wine forbids the entire mixture in any amount whatsoever, and it is never nullified. Rabbi Meir holds that the same law applies here as well, and therefore everything is forbidden. The Sages disagree: although it is true that a tiny drop of yayin nesech forbids an enormous quantity of kosher wine, here there is not even a single drop of forbidden wine in substance, only a taste absorbed in the walls of the vessel. In such a scenario they were lenient and ruled that there is no prohibition of benefit here, only a prohibition of drinking.
It is worth clarifying: normally taste is absorbed only through heat, and no heat is involved in storing wine. However, there is a separate rule - when something remains in a vessel for an extended period, roughly twenty four hours or more, we assume that the vessel absorbed its taste. Since the gentile stored his wine there for a long period, we assume that taste was absorbed, and rinsing the vessel does not help, because some of that taste seeps back out into the kosher wine and forbids it.
The halachah follows the Sages, as it will in all three cases: it is forbidden in eating but not forbidden in benefit. In a situation where the vessel is never used with heat, and a person wishes to kasher it because of the absorbed taste, the method of kashering is filling and emptying: one fills the vessel with water, leaves the water inside for twenty four hours, pours it out, and repeats this three times in total. In this way all the taste in the walls and in the bottom is considered to have been drawn out, and the vessel may be used for cold items.
The second dispute - grape pits and skins:
The second case is "hachartzanim v'hazagim shel ovdei kochavim" - the chartzanim and the zagim of gentiles. After a gentile trod on his grapes the wine became forbidden, and he is also left with chartzanim and zagim - the chartzanim are the seeds and the zagim are the skins (and some reverse the two translations). The question is whether the halachic status of the skins and the seeds is like that of the wine.
According to all opinions, as long as they are still moist they are forbidden, since the moisture in them is wine. The discussion is about a situation where they dried out completely, after twelve months. Rabbi Meir is stringent: "asurin, v'issuran issur hana'ah - divrei Rabbi Meir" - they are forbidden, and their prohibition is a prohibition of benefit, for in his view the skins and the seeds have the status of the grape juice, and once they were handled by a gentile they are forbidden forever. "V'Chachamim omrim: lachin asurin, yeveshin mutarin" - and the Sages say: while moist they are forbidden, once dry they are permitted. The skins and the seeds are not included in the prohibition at all; as long as they are moist they are forbidden because of the wine in them, but once they have dried out completely they are permitted even in eating. The halachah follows the Sages.
The third dispute - morayes and the cheeses of Beis Unyaki:
Morayes: although the Mishnah groups the two items together, these are two separate matters. Morayes is a type of seasoning that was in use in the Roman period: the leftovers of fish processing - the oil and the innards - mixed with salt and left to dry out, and at times they would add to the mixture not only water but even wine. (It is worth noting that morayes is the inferior and unappealing version, while the high quality product, garum, was an extremely expensive seasoning in the Roman period.) The question is whether morayes prepared by gentiles is forbidden on account of the wine they added to it.
The wine is not added for flavor: murayes is essentially rotting fish innards, repulsive and foul smelling, and the wine is there to take the edge off. Nobody wants the taste of the wine for its own sake, and so we have to ask whether this wine counts as imparting a forbidden flavor. Rabbi Meir holds that the wine is present and the mixture is therefore forbidden even for benefit, while the Sages were not so stringent: there is a prohibition against eating it because the wine is present, but no prohibition against benefit, since the wine is not there in its own right but is dissolved into the mixture in a small quantity, and its taste is of no significance.
The cheeses of Beis Unyaki: Beis Unyaki was a gentile city, where most of the calves were ultimately offered to idols. To follow the discussion one needs to understand how cheese is made: one takes a ruminant that has died - a cow, a goat or a sheep - which has four compartments in its stomach. In the last of them, called in Hebrew the keivah, there is milk that has curdled and set, because that is where the enzyme rennin is found, which curdles milk and turns it into cheese. This substance, itself also called keivah (in English, rennet), is extracted from the walls of the stomach and is not considered part of the animal but a kind of waste product, and it is used to curdle milk into cheese.
As far as ordinary kashrus is concerned, we do not worry about the keivah even if it comes from a non-kosher animal, since it is not considered part of the animal at all. But an animal that was offered to idolatry - everything offered becomes forbidden for benefit, including the stomach inside it. Hence the question: should we be concerned that the keivah used to make the cheese came from an animal offered to idolatry, in which case the cheese would be forbidden in any amount.
Rabbi Meir is always concerned for the minority: even though only a minority of the animals from which the keivah came were actually offered, since most of the calves in that city are offered, he is concerned and forbids it. The Sages are not concerned: even though most of the calves in Beis Unyaki are offered to idolatry, only a minority of the keivah supply comes from those offerings, and therefore they were lenient about cheese made there. Nevertheless the Sages agree that the cheese may not be eaten, because of the rabbinic prohibition of gentile cheese - perhaps they also used meat from the stomach itself to curdle the milk.
In the words of the Mishnah: "Murayes u'gevinos Beis Unyaki shel ovdei kochavim - issuran issur hana'ah" - this is the view of Rabbi Meir, that they are forbidden even for financial benefit, because of the concern that the cheese came from the keivah of an animal offered to idolatry. "V'Chachamim omrim: ein issuran issur hana'ah" - there is nothing here but a prohibition against eating, because of gentile cheese, and one may sell it to a gentile and keep the proceeds.
In summary: the three disputes in the Mishnah - gentile skins and jugs into which a Jew put his wine, grape seeds and skins that have dried out, and murayes and the cheeses of Beis Unyaki - all turn on the same point: Rabbi Meir is stringent and forbids benefit, while the Sages are lenient and limit the prohibition to eating alone. The halachah in all these cases follows the Sages and not Rabbi Meir.