Mikvaos, Chapter 6, Mishnah 6. This mishnah presents a striking situation: a person (or a vessel) has already undergone a completely valid maaseh tevilah, a proper immersion, and yet on the way out of the water he picks up tumah all over again. The Mishnah teaches us in which circumstances that happens, and how one arranges matters so that the exit from the mikveh does not undo what the immersion accomplished.
The background: a kli cheres conveys tumah through its airspace
One halachah about pottery has to be in place before the mishnah can be read. A kli cheres, an earthenware vessel, that has become tamei is metamei me'avirah: anything that enters the hollow space within it contracts its tumah, and no touching of the walls is required at all. An adam, a person, is not affected by this route of tumah. Keilim and ochlim, though, vessels and foodstuffs, do become tamei the moment they are held within such a space.
Add to this a second halachah: immersion accomplishes nothing for pottery. Once an earthenware vessel has taken on tumah, no mikveh in the world will purify it. Even while it lies submerged in the mikveh water it is still a kli cheres tamei, fully able to pass on its tumah to whatever occupies its hollow.
The case of the gistron
Our mishnah pictures a gistron, a fragment left over from a shattered earthenware vessel, resting in a mikveh. Someone has keilim in need of purification, and rather than dipping them in the open expanse of the mikveh he dips them inside this shard.
"Gistron shebamikveh, v'hitbil bo es hakeilim, taharu mitumasan, aval temeim al gav kli cheres"
As far as the immersion goes, nothing is wrong. The water resting in the gistron is continuous with the surrounding mikveh, so it does not count as water in a vessel at all; it is simply mikveh water, and the keilim are released from their tumah. The difficulty arises only when they are drawn out. Picture the shard positioned so that its edge rises higher than the surface of the water. Lifting the vessels out means carrying them up through the hollow of the pottery at a point where that hollow is no longer underwater, and the droplets clinging to them are then sitting inside the space of a kli cheres tamei. Those droplets contract tumah, and they pass it straight back to the vessels that had just been purified. That is why the mishnah declares them tamei because of the earthenware.
When the water covers the rim
"Im hayah hamayim tzafim al gavav kol shehen, tehorim"
Where the edge of the gistron is not exposed at all, with the mikveh water standing over it by however small a measure, the keilim stay tahor. The entire hollow of the shard lies beneath the surface, so the vessels are never held inside the space of pottery outside the water. They move from mikveh water into mikveh water without interruption, and the earthenware is given no opening to affect them.
The parallel case: a spring flowing through a tanur
The same rule is now applied to a second scenario. A ma'ayan, a spring, runs out through a tanur, an earthenware oven that is tamei, and a man steps down into that oven to immerse himself.
"Hu tahor, v'yadav temeios"
He himself comes up tahor. His immersion is a valid one, because what fills the oven is the flowing water of the spring, and in any event the hollow of a kli cheres has no effect on a person. His hands are a different matter: they are tamei, since a kli cheres tamei is able to render yadayim, hands, tamei even where it cannot do so to the man himself. And here again the mishnah has in mind an oven whose sides stand higher than the surface, so that raising his hands brings them up into the exposed hollow of the pottery.
Should the water lie over the oven, however, so that his hands, even when he lifts them, are still submerged and higher than the pottery's edge, they too are tahor. They never enter the uncovered hollow of the earthenware, and nothing of the oven's tumah can reach them.
The lesson of the mishnah
A single idea ties the two halves together. Earthenware that has become tamei holds onto that tumah even while lying beneath the water of a mikveh, and the risk it poses is located exactly in the open space above the surface, in the act of coming up. Where the water blankets the vessel entirely, leaving no exposed hollow to be crossed, the immersion is not merely valid; nothing is left behind that could undo it.