Sukkah, Chapter 1, Mishnah 6. Before us is a further discussion of which material is valid for use as sechach, and the Mishnah teaches us a dispute regarding covering the sukkah with boards.
The words of the Mishnah: "Mesachech bah nesarim - divrei Rabbi Yehudah, v'Rabbi Meir oser" - one may cover the sukkah with boards, these are the words of Rabbi Yehudah, and Rabbi Meir forbids it. Rabbi Yehudah holds that one may use nesarim, which are boards, as sechach, while Rabbi Meir forbids using them.
Which boards are they arguing about?
The Gemara explains and distinguishes between the measurements:
Four tefachim wide and more: invalid according to all opinions. Even though the material itself is the correct material, a board of such a width resembles the roof of a house. Four tefachim is the measurement of a significant place, a meaningful amount of area in halachah, and therefore it is no longer considered sechach but rather roofing.
Less than three tefachim: valid according to all opinions, both according to Rabbi Yehudah and according to Rabbi Meir. It is nothing more than an ordinary stick, and this is a perfect example of sechach.
Between three and four tefachim: here they disagree. Rabbi Meir holds that once the board has exceeded the width of a lulav - which is anything less than three tefachim - it is no longer considered sechach but a board and roofing material, and therefore it is invalid. Rabbi Yehudah disagrees and holds that only when it reaches a width of four tefachim, when it is genuinely roofing material, is it invalid; but with less than that it is valid.
Dofen akumah (a bent wall):
The Mishnah concludes with an interesting halachah, which introduces us to the principle of dofen akumah. Dofen akumah is a halachah l'Moshe miSinai - something that was transmitted and received from the giving of the Torah as part of the Oral Torah. Its content: when there is invalid sechach at the edge of the sukkah, next to the wall, it may be there for up to four amos, provided that one does not sit beneath it.
Even though ordinarily the sechach is required to be within three tefachim of the wall, the principle of dofen akumah establishes that we view the wall of the sukkah as though it bends and rises to meet the valid sechach, even though that valid sechach may be as far as four amos away from it. For this reason one may not sit beneath the invalid sechach, since with regard to it the wall is considered to bend over that area and meet the valid sechach.
The Mishnah brings an example of this: "Nasan aleha neser shehu rachav arba'ah tefachim - kesheirah, u'vilvad shelo yishan tachtav" - if he placed upon it a board that is four tefachim wide, it is valid, provided that he does not sleep beneath it. As has been explained, a board four tefachim wide is not valid sechach according to all opinions, and nevertheless the sukkah is valid, provided that he does not sleep - and for this purpose also does not eat - beneath that area.
The Mishnah is dealing with a board that is four tefachim wide or more, and the law is that the sukkah is valid up to four amos. This measurement is not mentioned explicitly in the Mishnah, but this is the halachah: up to four amos it is valid, provided that one does not sit beneath that area, since we view the wall of the sukkah as meeting the valid sechach and bypassing, as it were, the invalid sechach that is up to four amos wide.
In summary: in this Mishnah we learned the dispute between Rabbi Yehudah and Rabbi Meir regarding covering a sukkah with boards: at a width of four tefachim it is invalid according to all opinions because it resembles the roof of a house, at less than three tefachim it is valid according to all opinions, and between three and four they disagree. We also studied the principle of dofen akumah, a halachah l'Moshe miSinai, according to which we view the wall as bending toward the valid sechach, and therefore the sukkah is valid even with invalid sechach of up to four amos, provided that one does not sleep or eat beneath it.