Masechet Chullin, Chapter 8, Mishnah 1. This entire perek is devoted to the laws of meat and milk. The Torah writes, "Lo tevashel gedi bachalev imo," you shall not cook a kid in its mother's milk. This verse appears three separate times in the Torah, and the chachamim understood each repetition to teach its own prohibition: one forbids cooking meat and milk together, one forbids eating meat and milk that were cooked together, and one forbids deriving any hana'ah, any benefit at all, from such a mixture.
Note the precise boundary of the Torah's law: the prohibition of the verse applies to meat and milk that were cooked together. Eating meat and milk that were never cooked together is forbidden as well, but that is assur miderabbanan, a prohibition instituted by the chachamim. Only cooking brings the matter into the realm of de'orayta.
Which meat is included
Our mishnah now defines what qualifies as meat for these halachot. "Kol habasar assur levashel bechalav," every kind of meat is forbidden to be cooked in milk, "chutz mibesar dagim vachagavim," except for the flesh of fish and of grasshoppers. For the purposes of this halachah, fish and grasshoppers simply do not carry the status of meat, and kosher fish and kosher grasshoppers may therefore be cooked and eaten together with milk.
Every other type of meat is forbidden, but not all of it on the same level. Some meats are forbidden with milk biblically and others only miderabbanan, and the mishnayot ahead in this perek will draw those lines out in detail. The practical difference is significant. Whatever is assur on the de'orayta level is also forbidden to cook and forbidden to benefit from. But meat that is forbidden with milk only rabbinically, chicken being the classic example, may be cooked together with milk for a purpose other than eating, and one is permitted to derive benefit from it. The chachamim extended their decree only to eating, not to cooking or benefit.
Meat and cheese on one table
"Ve'assur leha'aloto im hagevinah al hashulchan." It is also rabbinically forbidden to bring meat up onto the same table as cheese or any other dairy food. The concern is straightforward: a person seated at such a table may let the cheese slip into a pot of meat standing there, and he will find himself cooking cheese together with meat, which is an issur de'orayta.
"Chutz mibesar dagim vachagavim." Fish and grasshoppers are the exception, and they may be set on the table alongside cheese without any concern whatsoever. At first glance this clause looks superfluous. We already know that fish and grasshoppers may be eaten together with milk, so why bother telling us that they may share a table with it? The chachamim answer that the mishnah is teaching us that these two are the only exceptions. Le'afukei, to exclude, meat that is forbidden with milk merely miderabbanan, such as chicken. Chicken too may not be placed on the same table as dairy, since a hot pot of it and a piece of cheese might well end up falling into one another and cooking together.
A vow against meat
The mishnah adds a further consequence of the fact that fish and grasshoppers are not classified as meat. "Hanoder min habasar, mutar bibsar dagim vachagavim." One who takes a vow not to benefit from meat may still eat fish and grasshoppers, because they are not meat.
Beit Shammai and Beit Hillel
The mishnah now returns to the question of meat and cheese on one table, and reveals that the ruling stated earlier is not unanimous. There is a machloket about exactly which meats may not be brought to the table with dairy.
"Ha'of oleh im hagevinah al hashulchan ve'eino ne'echal, divrei Beit Shammai." Beit Shammai hold that the flesh of a bird, chicken for instance, may indeed be set on the table together with cheese; it is only the eating of the two together that is forbidden. "Beit Hillel omrim, lo oleh velo ne'echal." Beit Hillel hold that it may neither be brought up onto the table nor eaten together with cheese. The ruling stated at the beginning of the mishnah, then, reflects the view of Beit Hillel.
"Amar Rabbi Yose, zo mikulei Beit Shammai umchumrei Beit Hillel." Rabbi Yose points out that this is one of the rare cases in which Beit Shammai are the lenient side and Beit Hillel the stringent one. Ordinarily the pattern runs the other way: Beit Shammai are the machmirim and Beit Hillel are meikel. Here the roles are reversed, with Beit Hillel forbidding chicken on a table with cheese and Beit Shammai permitting it.
Which table?
Finally the mishnah defines the decree precisely. "Be'eizeh shulchan amru? Amru, beshulchan she'ochel alav." Which table were they speaking about? A table upon which a person actually eats. "Aval beshulchan shesoder alav et hatavshil, noten zeh betzad zeh, ve'eino choshesh." But on a table used for arranging and preparing the food, the kitchen counter or island where a person sets out what he is about to serve, he may place meat on one side and cheese on the other and need not be concerned at all.
The distinction rests on how the food is handled. At a table where people are eating, food is in constant motion: dishes are shifted, hands reach across, portions are lifted onto forks. That is where the chashash lies, the real worry that dairy will end up in a hot piece of meat and be cooked with it. Where a person is merely arranging food before it is served, there is no such concern, and meat and cheese may be set out together on that table, provided that they are not touching one another.