Keilim, Chapter 22, Mishnah 1. This chapter turns our attention to furniture, and it opens with the table. To appreciate the Mishnah, we need one background principle first.
A keli made of wood becomes tamei only when it has a receptacle, a place in which something can be contained. A flat wooden board, having nothing to hold, is not the sort of wooden utensil that receives tumah by Torah law. And yet a wooden table does become tamei, on the level of a takanah deRabbanan, because a table is built precisely in order to keep things resting upon it. In a certain sense it functions as a container: its surface holds and keeps whatever is set down on it. That is enough for the Rabbanan to have given it the status of a keli that can become tamei.
The Mishnah's case
Once the table's status rests on its ability to hold food, the natural question is what happens when the table is altered. If the surface is damaged, or if it is no longer the original wooden surface, does it still carry its original status? That is exactly what our Mishnah addresses.
"Hashulchan vehadelufki shenifchatu": the Mishnah speaks of two pieces of furniture. The shulchan is the ordinary table at which people eat. The delufki is a serving board or platter used alongside it: the food would be arranged on the delufki and then brought over to the main table. Both of them, says the Mishnah, were nifchatu, meaning that portions of them broke away and were lost.
"O shechipan beshayish": or, alternatively, they were not broken at all, but portions of their surface were overlaid and covered with marble, so that the original wood is no longer exposed there.
"Veshiyer bahem mekom hanachat hakosot": in either case, there remained of the original wooden surface, the part that was neither broken off nor covered over, an area large enough for setting down the cups used for drinking.
"Teme'im": in such a case the table and the delufki remain able to become tamei. As long as some meaningful piece of the original wooden surface still serves its original purpose, the keli has not lost its identity. It continues to be the same table it always was, and it keeps its status as a wooden utensil that can receive tumah.
Rabbi Yehuda's standard
"Rabbi Yehuda omer, mekom hanachat hachatichot." Rabbi Yehuda is not satisfied with room for cups alone. In his view the remaining surface must be able to hold the pieces, that is, portions of meat and of bread, in addition to the cups.
The logic behind his position is that the table's whole claim to being a keli comes from its role in holding food. Room for a few small cups does not yet make it a table. Only when the surviving surface can still perform a table's real function, bearing the food itself, does the keli retain the identity it had before it was broken or overlaid, and with it the ability to become tamei.