The joyous holiday of Purim celebrates the salvation of the Jews from the wicked Haman, through the leadership of Queen Esther and her cousin Mordecai. Purim takes place on the 14th day of Adar, the 12th month of the Jewish calendar. (In the case of a leap year, it takes place in the 13th month, Adar II, while a minor holiday, Purim Katan, takes place in Adar I.) It usually falls in March. In 2015, Purim begins at sundown on March 4.
The carnival-like atmosphere of Purim, wearing of costumes, and bringing gifts of food door-to-door sometimes leads to it being referred to as the "Jewish Mardi Gras" or "Jewish Halloween" by non-Jews.
The story of Purim is found in the Biblical book of Esther, often referred to as "the Megillah." This is publically read in synagogues twice on Purim: when the holiday begins at nightfall, and the following morning. When the name of Haman is read, people stomp their feet, hiss, boo, or shake noisemakers to obliterate his name.
The story takes place in the Persian Empire, which extended to 127 provinces. In the third year of his reign, King Ahasuerus threw a lavish party, to which he summoned his wife, Queen Vashti, to display her beauty. When Vashti refused to obey his command, he had her killed for insubordination.
Regretting this decision after sobering up, Ahasuerus began a kingdom-wide search for a new queen, adding a member to his harem every night, but not finding a suitable replacement until Esther—a beautiful Jewish girl—was brought before him. He fell in love with her and made her the new queen. She had not wanted to be part of the search, and would not tell him anything about her background.
Soon after this, Haman became the chief advisor to Ahasuerus. He felt slighted by Mordecai, a Jew who refused to bow to him (and who, unknown to him or the king, was Esther's cousin). He obtained permission from the king to send out a decree to the entire kingdom calling for all the Jews to be wiped out on the 13th of Adar. He chose this date, which he hoped would be auspicious, using lots. (The Persian word for lots was pur; the holiday of Purim gets its name from this event.)
Mordecai sent word to Esther about this decree, and called upon her to intercede with the king. This was a risky move for Esther; it was forbidden to see the king without first being summoned, and he had after all killed his previous wife for not obeying his orders. Nevertheless, she accepted that she needed to take action. She called for a three-day fast among the Jews in the city, after which she went to see the king. She found favor in the king's eyes, and he offered to give her anything she wanted.
After a couple of subplots involving Mordecai and Haman fell into place, Esther informed the king that Haman was, in fact, plotting to kill her and all of her people. Incensed, the king ordered Haman to be hanged, and installed Mordecai in his place. While the original decree could not be rescinded, Mordecai was able to send out a second decree calling upon the Jews to defend themselves and kill their enemies. This they did, routing all opposition on the 13th of Adar, and celebrating on the 14th. This celebration on the 14th is now observed annually, on Purim.
In the capital city of Shushan, the Jews were given a second day to rout their enemies, on the 14th. They then feasted on the 15th. In commemoration, in Shushan, and in cities that were walled at the time of Joshua, Purim is celebrated on the 15th of Adar; this date is generally known as "Shushan Purim." Practically speaking, this now applies to Jerusalem.
The traditional observances of Purim include public readings of the Book of Esther, feasting, gifts of charity to the poor, and gifts of food among friends. It is also unique among Jewish holidays in that adults are encouraged to drink until they can't tell the difference between the phrases "cursed be Haman" and "blessed be Mordecai." Other popular activities include staging comedic plays, expounding on the Torah in humorous ways, dressing up in costumes, holding beauty contests, and marching in parades.
The general topsy-turvy spirit of Purim is ascribed both to the merry celebration of the occasion, and as an allusion to how the decree against the Jews was suddenly overturned, and their standing in the kingdom went from outcast to privileged.
As with many holidays, Purim has a food of its own: hamantaschen. Literally "Haman's pockets," these triangular cookies are said to resemble Haman's three-cornered hat. These traditionally contain poppy-seed or prune fillings, but other fruit fillings are also popular. (I'm a fan of cherry, myself.)
Purim is preceded by a minor fast, the Fast of Esther, commemorating the three-day fast that preceded the miracle of Haman's downfall. This is normally observed from dawn to sundown immediately before Purim. However, when this would conflict with Sabbath observance, it is moved to the preceding Thursday.