Welcome to Maseches Pesachim, Chapter 1, Mishnah 1. The chapter opens with the laws of bedikas chametz - the search for chametz on the eve of Pesach.
The words of the Mishnah:
"Or l'arba'ah asar" - the night of the fourteenth of Nissan, the night that leads into the fourteenth day.
"Bodkin es hechametz l'ner" - a person is obligated to search his premises for chametz by the light of a candle.
"Kol makom she'ein machnisin bo chametz ein tzarich bedikah" - a place into which people are not accustomed to bring chametz is exempt from the search, since it is not common or usual to bring chametz into such a place.
The Mishnah's question - two rows in the cellar:
On the basis of this principle the Mishnah asks: "V'lamah amru shtei shuros bamartef?" - There was a tradition in our hands, already before the Mishnah, that one must search two rows in the wine cellar. Yet a wine cellar would seem to be a storage area, and it is not a person's way to bring chametz in there.
To this the Mishnah answers: "Makom shemachnisin bo chametz" - the reference is to an area of the cellar into which chametz is occasionally brought. The Gemara explains: the attendant serving at a meal, when the wine runs out and he needs to go down to the cellar, may be in the middle of his own meal with a slice of bread in his hand, and leave it there by mistake. It turns out, then, that the wine cellar is indeed sometimes a place into which chametz is brought.
The question now under discussion is which two rows are meant, when it is stated that two rows in the wine cellar require searching and no more.
The opinion of Beis Shammai:
"Beis Shammai omrim: shtei shuros al pnei kol hamartef" - two rows that extend across the entire wine cellar. The Amoraim in the Gemara disagree as to what this means:
The front vertical row of barrels at the entrance, and alongside it, at a ninety degree angle, the horizontal row above - something like the shape of an upside down letter L: the rows running to the end of the cellar and the rows descending downward.
Only the first two vertical rows require searching.
The opinion of Beis Hillel:
"U'Beis Hillel omrim: shtei shuros hachitzonos shehen ha'elyonos" - there is no need to search two full rows, but only the two outermost rows.
The Amoraim disagree about the definition of these two outer rows as well. Since the outer upper row belongs both to the horizontal plane and to the vertical plane, the question is in which of the two directions the second row is measured:
The outer upper row and the one behind it - both on the horizontal plane.
The outer upper row and the one beneath it - both on the vertical plane.
In summary: In this Mishnah we learned the obligation to search for chametz on the night of the fourteenth by candlelight, and the principle that any place into which chametz is not brought does not require searching. On the basis of this principle the Mishnah challenged the obligation to search two rows in the cellar, and answered that it too is a place into which chametz is brought, as in the case of the attendant who goes down to the cellar with a slice of bread in his hand. Beis Shammai and Beis Hillel disagree about the definition of the two rows, and within each of the two views the Amoraim in the Gemara disagree between the horizontal plane and the vertical plane.