Once upon a time (because these things should start this way, even if they don't actually do so), there was a Persian king named Ahashverosh. For plot reasons, he decided to have a big party with his subordinate princes and such that lasted many days. On the seventh day, after Ahashverosh had been hitting the wine pretty hard, he summoned his wife, Vashti, to come down to the party so he could show her off. Vashti, oddly-independent woman that she was, refused (apparently she didn't like being objectified, who knew?). The inebriated king had her put to death, only to realise afterwards that he was left with no queen. So, he sent out a kingdom-wide search for a new queen.
Mordechai sent his niece Ester, who he's raised as his own daughter, to try for the post, since she was very pretty and had a brain, but told her not to tell anyone she was Jewish. Ahashverosh fell in love with her and married her, and Mordechai stopped by the palace every day to see how she was doing. On one such day he crossed the path of Haman (*noise*), the king's top advisor. Haman (*noise*) had a bit of an ego problem, and expected everyone to bow down before him. Mordechai refused, though, because it's against Jewish law to bow before another human. Haman (*noise*) must have had anger issues, too, because he decided to have all the Jews in Persia put to death. He chose lots (purim means "lots" in Hebrew) to decide a day to have them all killed off, and then told Ahashverosh that the Jewish people were dangerous and needed to be destroyed (familiar?).
Ahashverosh continued to show no common sense, and agreed to Haman's (*noise*) plan, sending out a decree that on the 13th of Adar (mid-March) the non-Jewish population of his domains was to rise up and kill they Jews in their midst, and the Jews were not allowed to fight back. Mordechai ran to Ester, and begged her to do something. She fasted for three days and then got dressed up and went before the king. Ahashverosh said that he loved her more than anything, and would give her half the kingdom if she asked, but Ester merely requested that the king and Haman (*noise*) come to a mini-banquet she was having. At the banquet, Ahashverosh repeated his declaration of love, but Ester told him and Haman (*noise*) to come to another banquet the next day. Haman (*noise*) went home, feeling all self-important, got pissed off when he ran into Mordechai camped out beside the gate, and made plans for a special gallows to hang Mordechai on (issues, this one has).
That night, Ahashverosh couldn't sleep, so he sent for the royal scribe to read him a bedtime story. The scribe talked about how a few years earlier Mordechai had saved Ahashverosh from a murder plot planned by two servants, but was never properly rewarded. Ahashverosh called Haman (*noise*) in, and asked how to properly thank a man who had done the king a great service. Haman (*noise*), thinking the king was referring to him, told the king that the man should be paraded through the streets on the royal steed dressed in royal robes, led by an official calling that this treatment was the reward for helping the king. Ahashverosh likes the idea, and tells Haman (*noise*) to set it all up for Mordechai the next day, with Haman (*noise*) leading the horse. Obviously, Haman was not happy about this.
(Now it must be noted that according to folk lore, Haman's daughter didn't know the role reversal, and dumped a bucket of slop on her father's head, thinking it was Mordechai. If I remember correctly, this doesn't actually appear in the Megillah, the scroll that contains the story.)
At the second banquet, Ahashverosh again declared his love for Ester, saying he would give her half his kingdom if she asked. (Yes, this is a rather repetetive story.) Ester told him that there was a plot to kill her and her people. Ahashverosh told her to tell him the villain who would do so murderous a deed (sorry, Crucible moment) and she pointed to Haman (*noise*), revealing that she was Jewish. Ahashverosh got really pissed and sentenced Haman to death by hanging on the gallows he'd built for Mordechai (yayfor dramatic irony). Ahashverosh could not cancel his earlier decree, so he instead changed it so that the Jewish people could fight back. On 13 Adar no one attacked, and on 14 Adar, the current celebrated date of Purim, there were big parties. And they all lived happily ever after, the end (because that's how these things should end, too).
Purim is observed for two days (14-15 Adar) everywhere except inside walled cities like Ahashverosh's capital (the only example of mention anymore is Jerusalem). People get dressed up in costume (my first was Ester, with one of the giant blue towels as my robes), give each other misholach manot (little gifts of cookies, fruit, and other sweets), go to noisy readings of the Megillah, and the adults get drunk to celebrate. At Megillah readings, noise is made whenever Haman's name is said (hence the "Haman (*noise*)" thing).