The items connected to idolatry that are listed below are forbidden, and not merely forbidden to eat but forbidden to benefit from at all: one may not derive any benefit from them whatsoever, not even indirect benefit such as selling them for profit. As to the force of this prohibition, there is room to discuss whether it is from the Torah or from the words of the Sages: the Gemara does bring a source for it from a verse, but the verse is from the book of Tehillim. Tosafos point out that we do not derive a Torah law from a verse in Kesuvim, but only from the Written Torah or from the Oral Torah, and therefore this is no more than a mere asmachta.
The verse to which the Mishnah alludes:
In Tehillim (chapter 106, verse 28) it says: "Vayitzamdu l'Ba'al Pe'or vayochlu zivchei meisim" - Israel attached themselves to the idolatry of Ba'al Pe'or and ate the offerings of the dead. On the face of it this is puzzling: why are these offerings called 'offerings of the dead', when they were brought to an idol and not to dead people? The plain meaning of the verse is that in contrast to the living God, the Holy One who is, as it were, alive and responds to those who call upon Him, an idol is like a dead thing and does not respond. The Gemara, however, expounds from the juxtaposition of the offerings to the dead: just as the body of a dead person is forbidden to benefit from, so too the offerings brought to an idol are forbidden to benefit from.
The items the Mishnah lists:
"Hayayin" - wine that we must suspect a gentile poured as an act of worship to his idol is yayin nesech and is forbidden to benefit from: not only to drink it, but even to derive any benefit from it at all, such as selling it. Beyond this prohibition there is also a rabbinic one: even 'stam yeinam', ordinary wine of gentiles about which we know of no libation, was forbidden by a decree of the Sages.
"V'hachometz" - this refers to vinegar whose origin is red wine, which began as wine and ended as vinegar. When that wine was in the possession of a gentile before it turned to vinegar, we must suspect that the gentile used it for an idolatrous rite, and it became forbidden from that moment. But if the vinegar was in the possession of a Jew and he sold it to a gentile, it is permitted to benefit from it: it was never wine in the hands of the gentile, and one does not offer sacrifices and meal offerings to an idol with vinegar.
"V'cheres ha'Adriani" - named for the emperor Hadrian, whose soldiers were stationed in Eretz Yisrael and persecuted the Jews terribly in the second century. The way this earthenware was made was that the clay was mixed not with water but with wine, and it was not fired in an oven but left to dry, until the wine was absorbed into it. Afterwards one could soak the earthenware in water and draw the taste out of it, producing a drink with the flavor of wine. Since the wine is present inside it and its taste comes out, the pieces of earthenware themselves are also forbidden on account of the status of the wine of idolaters.
"V'oros levuvin" - processed animal hides that have a hole in the place of the heart (levuvin from the word lev, heart). According to the first Tanna, a hole around the heart indicates that the animal was alive and the idolater tore out its beating heart while it was still living and offered the heart, and by this the entire animal became like an offering, so that even its hide is forbidden to benefit from. But the Mishnah qualifies that this depends on the shape of the tear: if the hole testifies that the animal served as an offering, it is certainly forbidden to benefit from; but if the shape of the cut does not point in that direction, and there is no way a beating heart could have been removed through it, we assume it was made for some other reason, and the hide is permitted to benefit from. In our times offerings of a beating heart are not found at all, and therefore this has no practical application.
Meat entering a house of idolatry and meat leaving it:
Meat - and the same applies to fish or fowl, except that meat is the choicest offering and is therefore the simple assumption - that is on its way to the house of idolatry and has not yet actually served as an offering is permitted. The reason: there is no designation and no consecration for idolatry, and one cannot designate something in advance to be an offering to an idol so that it should become forbidden. Once it has actually been used, it becomes forbidden; and likewise if there is a concern that it was already used, it is certainly forbidden. But before it has arrived there, it certainly has not yet been presented, and therefore it remains permitted.
By contrast, "hayotzei asur" - meat leaving a house of idolatry is forbidden to benefit from, even if all the signs indicate that this animal never served as an offering or a meal offering, since one never knows what goes on inside those temples. And the reason for this is: "mipnei shehu k'zivchei meisim" - an allusion to the verse in Tehillim cited above. Meat leaving a pagan temple has the law of sacrificial meat, which is forbidden to benefit from once it has been offered to an idol. These are the words of Rabbi Akiva.
"Ha'holchin l'Tarpus":
The final point of the Mishnah returns to and is closely bound up with the first Mishnah of the tractate. Idolaters who are going on pilgrimage to their pagan festival - the word 'Tarpus' is a term of derision hinting at disgrace, filth and debauchery, and cannot be translated literally, and the reference is to their festivals and their bacchanalian revelries - "asur laseis v'laseis imahem". One may not do business with them on their way to the festival, out of concern that they will attribute their business success to their god and praise his name, a prohibition we already saw in the first chapter. But "v'haba'in mutarin": on their way back from the festival, according to the approaches we saw in the first Mishnah of the tractate, there is no concern that they will retroactively attribute anything to the idol, and therefore it is permitted to do business with them on their return.
In summary: In this Mishnah we learned the list of items whose prohibition is a prohibition of benefit - wine, vinegar that began as wine in the hands of a gentile, Hadrianic earthenware and pierced hides - and the source of the prohibition in the verse "vayochlu zivchei meisim", which compares offerings of idolatry to a corpse, from which one may not benefit. We also examined the distinction between meat that is entering, which is permitted because there is no designation for idolatry, and meat that is leaving, which is forbidden because it is like offerings of the dead, and the distinction between those going to Tarpus, with whom it is forbidden to do business, and those returning from it, with whom it is permitted.