The battles fought between the Jews and their enemies throughout the Persian empire took place on Adar 13th. Around the world, the Jews rested and celebrated on the following day—the 14th of Adar. In the capital city of Shushan, however, where there were a greater number of Jew haters, the fighting continued for two days, Adar 13 and 14. The victory celebrations in Shushan were thus held on the 15th of Adar.
When the holiday of Purim was set for the 14th of Adar, the sages instituted that Shushan residents perpetually observe Purim on the 15th of Adar—the day when the Shushanite Jews celebrated. The 15th of Adar is hence known as "Shushan Purim."
Along with Shushan (which is located in modern-day southwestern Iran), all cities that were walled at the time when the Joshua-led Israelites entered Canaan, observe Purim on the 15th.1
Today the only city that we are certain had walls in Joshua's times is JerusalemToday the only city that we are certain had walls in Joshua's times is Jerusalem.2 And indeed, in the Holy City, Purim is festively celebrated one day after all other cities.3 There are a number of other ancient cities in Israel – such as Jaffa and Tiberias – regarding which there is a reasonable doubt whether they were walled in Joshua's times. These cities observe two days of Purim.
Three-Day Purim
Adar 14 – the "regular Purim" – can never fall on Shabbat, but Adar 15 can. For the residents of Jerusalem, this results in the unique phenomenon of a "Triple" or Three-Day Purim. Because a number of the Purim mitzvot cannot be performed on Shabbat, the observances are spread over a period of three days.
Friday:
Megillah reading4 night and day. Gifts to the poor during the daylight hours of Friday.5
Shabbat:
The Purim V'al Hanissim is added to all the day's prayers and Grace after Meals. The maftir of the day is the Purim Torah reading, and for the haftorah we repeat the story of Saul and Amalek—that was read last week on Parshat Zachor.
Sunday:
We send mishloach manot6 and enjoy the Purim feast7 during the daylight hours of Sunday.
Solidarity with Jerusalem
"It would therefore be fitting and good, very good, that on this Sunday [when Jerusalemites celebrate the 'third day of Purim'] Jews everywhere should add in joyful activities: words of Torah (which 'gladden the heart'), gladdening other Jews with a feeling of love, and, if fitting or necessary, through sending mishloach manot and giving gifts to the poor...
"And through this all to further unite with Jerusalem, to which we turn daily during the course of every prayer: 'and they will pray to G‑d by way of the city that You chose8'—chosen and given to each and every Jew forever, an eternal inheritance."9