Keilim, Chapter 25, Mishnah 1. This mishnah introduces a rabbinic decree known as achorayim v'toch, literally "the outside and the inside" of a utensil. The decree teaches that on a deRabbanan level, when we are dealing with tamei liquid, the outer surface of a keli and its inner surface are treated as two distinct areas with two distinct sets of laws.
What does that mean concretely? Should tamei liquid reach the inner surface, tumah spreads through the entire keli, exterior included. Should the liquid settle on the exterior alone, however, the tumah is confined there: only that outer face becomes tamei, while the inner face of the utensil stays tahor.
Which utensils are included
Our mishnah begins with a broad rule that covers everything: "Kol hakeilim", every utensil, "yesh lahem achorayim v'toch", is governed by the distinction between exterior and interior. In practical terms, tumah from liquid resting on the outer face is restricted to that face, and the inner face is left unaffected.
The mishnah then gives examples: "kegon hakarim v'hakesatot v'hasakim v'hamartzufin" - such as pillows, cushions, sacks and large packing cases. What these items share is that they can be turned inside out; there is nothing structurally fixed about which side faces the world. Even so, Rebbi Yehuda holds that the two surfaces are still considered separate parts for the purposes of this decree.
Rebbi Meir: only when there are loops
Rebbi Meir narrows the ruling considerably. He states "Kol sheyesh lo tovarot", whichever of these items is equipped with tovarot, and only such items, "yesh lo achorayim v'toch", come under the law of exterior and interior. Tovarot are loops, much like the loops found on a belt, which were stitched onto the outer face of a pillow or a sack; a cord was threaded through them and drawn tight, so that the item closed up and whatever was stored in it stayed put.
The logic is straightforward. A utensil fitted with loops will always be used with the loops facing outward, and it will therefore never be turned inside out. Its exterior is permanently the exterior and its interior is permanently the interior, so it makes sense to speak of an "outside" and an "inside" that carry separate laws.
He then states the reverse side of his rule: "v'chol she'ein lo tovarot", whichever of them carries no loops, "ein lo achorayim v'toch", is excluded from this rabbinic tumah altogether. Such an item can be flipped around whenever its owner pleases, so neither face is truly its exterior and neither is truly its interior, and the decree is left with nothing to apply to.
Flat surfaces: the table, the serving table and the tray
From cloth and leather containers the mishnah moves to a different sort of item: "hashulchan v'hadulbeki", a dining table and a dulbeki, which was a smaller stand used for serving. Of these the mishnah rules "yesh lahem achorayim v'toch", that they too fall under the law of exterior and interior, and it adds "divrei Rebbi Yehuda", marking this as Rebbi Yehuda's view. The ruling is surprising, for a table is flat and encloses nothing, so at first glance it possesses no interior whatsoever. Rebbi Yehuda's understanding is that the upper face serves as the interior, since that is the side on which anything set down there rests, while the underside plays the role of the exterior.
Rebbi Meir responds: "Ein lahem achorayim" - tables have no "outside" in this sense, and the decree of achorayim v'toch does not apply to them. They are flat, they form no receptacle, and so there is no basis for splitting them into two halves with two different laws.
The mishnah closes with a parallel case: "v'chein tavla she'ein lah livzbez" - and the same dispute applies to a tray that has no rim. Lacking a rim, such a tray holds nothing within it and has no natural inside or outside. Rebbi Yehuda would say that its upper surface counts as the inside and its underside as the outside, so that the law of achorayim v'toch does apply. Rebbi Meir maintains that it is simply a utensil with no outside and no inside, and the decree does not touch it.