Megillah, Chapter 3, Mishnah 2. In the opening Mishnah of the tractate we learned that the Megillah is read on the eleventh, the twelfth, the thirteenth, the fourteenth or the fifteenth of Adar. Our Mishnah comes to explain how this works out in practice, and to spell out the division of the days according to the day of the week on which the fourteenth of Adar falls.
The principle of "the day of gathering":
The villagers would come into the large towns on Mondays and Thursdays, since those were the days on which the courts convened. Because they were not proficient enough to read the Megillah themselves and needed someone to read it for them, the Sages made it easier for them and allowed them to hear the Megillah on the days they were coming to town anyway - the "day of gathering" (yom ha'knisah).
The order of the days in the Mishnah:
"Chal lihyos yom arba'ah asar ba'sheni" - if the fourteenth falls on a Monday, the fourteenth itself is a day of gathering, and therefore "kefarim va'ayaros gedolos korin bo ba'yom" - the villages and large towns read on that very day, while "mukafos chomah le'machar" - the walled cities read the next day, the fifteenth, which is Tuesday.
"Chal lihyos ba'shelishi o ba'revi'i" - if it falls on Tuesday or Wednesday, "kefarim makdimin le'yom ha'knisah" - the villages read earlier, on the day of gathering: if the fourteenth falls on Tuesday, the villages read on the thirteenth, and if it falls on Wednesday, they read on the twelfth. "Va'ayaros gedolos korin bo ba'yom" - the large towns read on that very day, Tuesday or Wednesday, "u'mukafos chomah le'machar" - and the walled cities on the following day, the fifteenth.
"Chal lihyos ba'chamishi" - if it falls on Thursday, this too is a day of gathering, and therefore "kefarim va'ayaros gedolos korin bo ba'yom" - the villages and the large towns read on that day, the fourteenth, "u'mukafos chomah le'machar" - and the walled cities on the next day, the fifteenth, which is Friday.
Two limitations at the end of the week:
The Megillah is not read on Shabbos, a decree lest a person carry it to someone proficient so that he read it for him, and thereby come to carry in a public domain on Shabbos. Likewise, the reading is not pushed off past the fifteenth, for the Sages derived from a verse in the Megillah that its time may not be passed over, and the fifteenth is the last day for the reading.
"Chal lihyos erev Shabbos" - if the fourteenth falls on Friday, "kefarim makdimin le'yom ha'knisah" - the villages read earlier, on the day of gathering, Thursday, which is the thirteenth, "va'ayaros gedolos u'mukafos chomah korin bo ba'yom" - the large towns and the walled cities read on that very day: the large towns read on Friday, the fourteenth, and the walled cities too - whose usual day is the fifteenth - read on the fourteenth, since the fifteenth falls on Shabbos, when the Megillah is not read, and it is also impossible to delay until Sunday, which is the sixteenth.
If the fourteenth falls on Shabbos - the Megillah is not read on Purim itself, and therefore both the villages and the large towns read earlier, on the day of gathering, Thursday, which is the twelfth. Even though the large towns could have read on Friday, since the villages are reading earlier and the reading is in any case moved off Shabbos, the towns read together with them on Thursday. The walled cities read on the day after Shabbos, Sunday, which is the fifteenth - their usual day.
If the fourteenth falls on Sunday - the villages read earlier, on the preceding day of gathering, Thursday, which is the eleventh of Adar. This is the case in which the eleventh comes into use. The large cities read on that very day, Sunday, which is the fourteenth, and the walled cities read the next day, Monday, which is the fifteenth.
In summary: This Mishnah explains how the days for reading the Megillah stretch from the eleventh through the fifteenth of Adar: the villages read earlier, on the day of gathering (Monday or Thursday), the large towns read on the fourteenth, and the walled cities on the fifteenth. When the fourteenth falls on Friday or on Shabbos, the order shifts because of the decree that the Megillah is not read on Shabbos, and because of the rule that the reading is not delayed past the fifteenth.