Avodah Zarah, Chapter Two, Mishnah 6. The Mishnah opens: "Eilu devarim shel ovdei kochavim asurin, v'ein issuran issur hana'ah" - the following items, when they come from idolaters, are forbidden to eat but not forbidden to derive benefit from. In other words, these are items forbidden by rabbinic decree, or in borrowed language: they are not kosher.
Two different reasons underlie these decrees:
A genuine kashrus concern - there is a real worry that the food is not kosher on a Torah level, because a forbidden substance has been mixed in.
The prohibition of intermarriage - even when we know that the ingredients are kosher and the utensils are kosher, the Sages forbade benefiting from these foods out of concern for chasnus, intermarriage. We do not want a Jew socializing with idolaters, picking up their bad habits, and ultimately coming to marry into their families. Some Rishonim seem to hold that this is not only a matter of intermarriage but also of cultural assimilation - absorbing the customs and attitudes of the gentiles.
Accordingly, each item on the list needs to be explained on its own terms.
"Chalav shechalavo oved kochavim v'ein Yisrael ro'ehu":
The first item on the list is milk that was milked by an idolater without a Jew watching, which is what is called chalav akum. Although the Mishnah speaks of idolaters, the law applies to milk that comes from any gentile, since the concern is that non-kosher milk may have been mixed in - donkey milk, camel milk, and the like. For this reason the Sages ruled that milk which was not supervised by a Jew is not kosher.
The supervision required here is minimal: it is enough that the Jew is present near the place of milking, and he does not have to see the gentile milking with his own eyes. It is enough that he is situated in such a way that he could get up and look at what is happening if he wanted to, and that alone is enough to deter the gentile, who knows the rules, from mixing in donkey milk or anything similar. Strictly by the law, and ideally, a Jew should supervise from the start of the milking, and check the receiving pail in advance to make sure nothing forbidden is in it.
Still, it is well known that a number of poskim, foremost among them Rabbi Moshe Feinstein, though he is certainly not the only one, ruled that government supervision which strictly deters dairy companies from adding forbidden substances is sufficient. On this basis, in the United States, where there are stringent regulations governing the milk supply and its contents, Rabbi Moshe permitted relying on this and drinking milk that was not under Jewish supervision, even though he himself was stringent about it. The observant community in America is divided on the question of chalav akum, while in Eretz Yisrael the dispute is far narrower, and most of the community simply relies on the lenient position. As a result, in Eretz Yisrael matters are easier across the board in all areas of kashrus.
"V'hapas":
The second item is bread baked by a gentile. Its prohibition is not because of a concern about forbidden ingredients: even when we know that the ingredients of the bread are kosher - flour, water, and eggs - and even when the utensils are presumed not to be bnei yoman, meaning they were not used with forbidden food in the past twenty-four hours, so that technically the bread is kosher, the Sages nevertheless said that one does not eat a gentile's bread, so that a Jew should not become friendly with them, absorb their habits, and marry their daughters.
As to the scope of this prohibition in practical halachah, there is a range of opinions. The custom of Klal Yisrael was to be lenient with what the Gemara calls pas palter, that is, a baker's bread, commercially produced bread: if it is known that the bakery uses kosher ingredients and kosher utensils, one may rely on that and buy bread produced in a gentile's bakery even without Jewish supervision. There is a discussion about the law when Jewish bread is available but is not of good quality. Even bread that does not come from a baker but from a private individual is permitted in certain scenarios, such as a pressing situation, or when no other food is available, as with someone traveling through a place. A full treatment of the practical halachah is beyond the scope of our lesson.
"V'hashemen":
Their olive oil was also forbidden. The Gemara explains that oil, like bread, was forbidden so that a Jew would not mingle with gentile society: once oil, bread and wine were forbidden, and these were the staple foods of that era, a Jew would no longer eat regularly with his gentile neighbors, since it simply would not be practical. Rabbi Yehudah HaNasi, the compiler of the Mishnah, together with his court in his generation, therefore annulled the prohibition on oil and permitted consuming oil even when it came from gentiles, because he saw that the community was not upholding this decree and had never accepted it.
Although the usual rule is that a later court cannot annul a rabbinic enactment of an earlier generation unless it is greater than it in wisdom and in number, which is rarely the case, another rule operates here: a decree that the community cannot uphold, or that never spread and was never accepted by the people, is not binding and may be annulled, and that is what happened here. In practice, someone living outside the large Jewish centers, let us say in Stockholm or Athens, walks into a store and buys pure cold pressed olive oil with no hechsher, and this is what everyone does, and the oil is considered entirely kosher - and this principle is what is being relied upon.
"V'hashlakos":
This term is hard to translate. Its literal translation is cooked vegetables, but that translation is misleading, because what is meant here is the entire body of restrictions known as bishul akum - food cooked and prepared by a gentile. Here too the issue is not kashrus but intermarriage and assimilation. It is important to emphasize that the restrictions of bishul akum apply only under two conditions: to foods that are not eaten raw, for if the food could be eaten raw the prohibition does not apply; and to foods fit to be served at important social occasions, such as a wedding feast - for if it is the sort of thing placed on the table to be eaten at such an event, even as a seasoning, it is forbidden when prepared entirely by gentiles.
There is a dispute as to how much Jewish involvement is enough to remove a food from the category of bishul akum, and this has many practical implications for how a mashgiach supervises restaurants and the like. In brief, there is a distinction between the Ashkenazic and Sephardic authorities:
The Ashkenazic position and the Rema: They are far more lenient. It is enough for the Jew to perform one small act, such as lighting the fire or tossing a twig into it as was done in the time of the Mishnah, and with that his involvement is considered sufficient.
The position of the Sephardic authorities and the Mechaber: Significant involvement by the Jew in the actual cooking of the food is required, and that is an entirely different world.
In any event, if the Jew cooked the food partially in a real way, it is not bishul akum, and the food is permitted provided it is kosher in all other respects.
From here the Mishnah returns to listing items whose concern is a genuine kashrus concern, a mixture of something forbidden:
"Uchevashim shedarkan liten l'sochan yayin v'chometz" - pickled foods. In the time of the Mishnah many foods were pickled, since there was no refrigeration. If the pickling recipe includes wine or vinegar derived from wine, we suspect that forbidden wine vinegar is mixed into the food, and it is therefore forbidden out of a real kashrus concern.
"Utarit terufah" - tarit fish that has been chopped into small pieces. As long as the fish can be identified, it is kosher; but once it has been chopped into pieces and crumbs, it is no longer possible to see what is mixed in, and perhaps crumbs of other, non-kosher fish got mixed in. Chopped fish is therefore not kosher, out of a legitimate concern for a forbidden mixture.
"V'tzir she'ein bah dagah kilbis shotetes bo" - tzir is the brine of pickled fish. The kilbis is a non-kosher fish, but if it swims and lives in the brine, that is a sign that the brine is kosher, since the kilbis can survive only in brine of kosher fish and not in brine of non-kosher fish. It is, in effect, a detector that identifies kosher brine. When no kilbis swims in it, we must suspect that the brine is not kosher, lest the juices of forbidden fish are mixed into it.
"V'chilak" - another type of fish, which is inherently kosher, except that when it is small it has no fins or scales, and the scales appear only as it matures. For that reason, when the fish are small and numerous, there is no way to verify that they are all indeed chilak fish, and perhaps other, non-kosher fish got mixed in with them, and such a mixture is forbidden.
"V'koret shel chiltis":
Chiltis is a type of spice, used to this day around the Mediterranean and in Yemenite cooking, and it is extremely sharp and pungent. The underlying halachah here is that a sharp item has the power to draw out flavors and revive them, even flavors that are more than twenty four hours old, even when the knife is clean and the food is cold. The most familiar example is the onion in the kitchen, and likewise radish and horseradish: if one cuts an onion with a dairy knife, the onion becomes dairy, and if the knife is treif, the onion becomes treif. So too with chiltis: if a gentile chopped it with his knife, which had previously cut forbidden items, we suspect that even though everything is cold and even though the knife has not been used within the past day, the power of the sharp item awakens the flavors and draws them out into the chiltis, which absorbs the forbidden flavor and becomes forbidden. For this reason one may not buy chopped chiltis. "Koret" means a small piece, like a grain or a kernel.
"U'melach sedomis":
This is a type of salt. The Bartenura explains that in Roman times there was a special salt, coarse and brilliantly white, that was considered a delicacy, and it was mixed with pig fat or with oils of forbidden fish, and this mixture was eaten as a seasoning among royalty - something like our caviar, grains of salt with the flavor of fish. Since we are concerned that actual pig fat or oils of forbidden fish are mixed into it, salkontit salt was forbidden, even though to the eye it is nothing more than salt.
To summarize: The Mishnah concludes: "Harei eilu asurin, v'ein issuran issur hana'ah" - all of these items are forbidden to eat, but not forbidden to derive benefit from, so one may, for example, sell them. In the last items the reason for the prohibition is the concern for a mixture of something genuinely forbidden, whereas in the first ones - and especially regarding food cooked by a non-Jew and bread baked by a non-Jew, and for a time also the oil of non-Jews until it was permitted - the reason for the prohibition is the fear of assimilation, intermarriage with non-Jews and learning from their ways.