Haman is appointed to some important post in Ahasuerus' court, and all the servants save Mordecai bow down to him. Because no human being has ever been able to mind his business for longer than 5 seconds, the other servants immediately start hassling him about it, especially since he told them he's an Israelite. They also snitch on him to Haman. You especially see this kind of behaviour between smokers and non-smokers in modern offices.
Of course, now that it has been pointed out to him, Haman has to get angry. At first he decides only to punish Mordecai, but there hasn't been a massacre now for like, 3 books, so of course Haman decides to wipe out the Israelites. He casts lots to figure out which day to start the massacre. Lots are called Pur, hence the festival of Purim.
He finally thinks to ask the king if he can start the first Holocaust, framing it in terms of There is a certain people scattered abroad and dispersed among the people in all the provinces of thy kingdom; and their laws are diverse from all people; neither keep they the king's laws: therefore it is not for the king's profit to suffer them (v. 8) which is pretty much the excuse given by every government in history to deport people it doesn't like, from Jews everywhere to Protestants in France to Muslims in modern-day Europe. The king is still distracted by his new harem of virgins, and he gives his blessing.
Finally, the day of killing arrives. Letters are sent to all the towns and villages, but the city of Shushan is perplexed.