The battles fought between the Jews and their enemies, which took place on Adar 13 throughout the Persian empire (see "Today in Jewish History" for that date), continued for two days -- Adar 13 and 14 -- in the capital city of Shushan, where there were a greater number of Jew haters. Thus the victory celebrations in Shushan were held on the 15th of Adar, and the observance of the festival of Purim was instituted for that day in Shushan and all walled cities. (See Laws and Customs below).
On this date, in the year following the Holy Temple’s destruction, G‑d tells Ezekiel to take up a lamentation for Pharaoh, king of Egypt, and for the Jewish nation’s other enemies, foretelling their ultimate downfall.
Read the prophecy here: Ezekiel ch. 32
In cities that are surrounded by a wall dating from the days of Joshua (13th century BCE) -- a prominent example is the city of Jerusalem -- the festival of Purim is observed on the 15th of Adar (instead of the 14th), in commemoration of the fact that in the ancient walled city of Shushan, the first Purim was celebrated on this day (see "Today in Jewish History").
All over the world, Tachanun is omitted due to the special joy of the day.
(For an overview of the Purim observances and links to more information, see "Laws and Customs" for Adar 14.)
A Jew entered the Alter Rebbe’s study and said, “Rebbe, I am a simple man. Please explain to me: What is this holiday of Shemini Atzeret?”
The Alter Rebbe held his head in his hands for a moment. Then he answered:
“For a long journey, you might make a concentrate of the food and drink you will need for the way. At every stop, you mix some of the powder with water, and you have enough for that day.”
“Shemini Atzeret contains all the joy for the entire year, but in highly concentrated form. Treasure every moment!”