How It All Goes Down
The Book of Esther begins with the Queen of King Ahasuerus—Vashti—snubbing the king's request to meet with her. Naturally, being a rather unstable fellow, Ahasuerus fires-slash-divorces her. Now he needs to pick a new queen and eventually manages to select Esther—a comely, young (secretly Jewish) woman who is a part of his harem.
As for her backstory, Esther's an orphan who was raised by her righteous cousin, Mordecai. When the king came looking for young virgins to possibly fill the role of his new queen, Esther made sure to jump into line. She wins favor with the people in the harem and eventually with the king himself, becoming queen. Moreover, Mordecai helps uncover a plot to kill the king, allowing Esther to warn him in time. This earns him some Brownie points as well.
But all is not well in the king's courts—treachery is afoot. When Mordecai refuses to bow down to the evil counselor Haman in the street, the evil, (probably) mustache-twisting counselor decides to engineer a plot to murder all the Jews in the Persian Empire. The plot basically involves Haman going to the king and saying, "I think we should kill all the Jews in the Persian Empire." And the king says (to paraphrase him), "Alright."
Haman walks away, twisting his mustache some more (probably), glad that the king has cottoned to his genocidal plans. The king doesn't know that his own queen is Jewish, because Esther's been keeping it secret. But the threat of the Jews' imminent demise kicks Esther and Mordecai into action. Mordecai goes and wails outside the palace gates while wearing sackcloth, and Esther fasts for three days before visiting the king.
Esther is worried the king will execute her for visiting him unannounced, but—to the contrary—he is mellow and pleased. He offers to give her whatever she wants. She asks him to have a banquet for her and Haman the next day. Then, after that banquet, she asks for another one on the following day. Meanwhile, Haman is excited about the massacre that's about to happen. He builds a huge gallows to hang Mordecai.
But his hopes are dashed the following morning, when the king—remembering how Mordecai saved his life—orders Haman to honor Mordecai and lead him in a parade through the town (which Haman very reluctantly does). At the second banquet, Esther asks the king to punish Haman for trying to kill her and her people—and the king does. Haman is hanged to death on the same gallows he had built for Mordecai (ironic, indeed). The Jews of Persia massacre all of Haman's agents and supporters (roughly 75,000 people in all), Mordecai is made into the king's new counselor, and Purim becomes an official Jewish holiday to celebrate. Good times, gang.