The Book of Esther officially makes Purim a holiday and tells all Jews, everywhere, to celebrate it. But it doesn't give an extensive glimpse of the actual customs of Purim itself—aside from saying that people should give food gifts to each other and also provide charity to the poor.
Sometimes people call Purim the "Jewish Halloween," but that's not actually a very technically accurate description. It does involve dressing up in costumes, but the bigger point of Purim is to see what the world would look like if everything were turned upside down. It's celebrating a day when everything went topsy-turvy and evil that seemed like it was about to win a victory over good was suddenly destroyed. Turns out, it looks like a pretty good time.
Traditionally, Purim involves lots of wine drinking and feasting, in addition to the costume-wearing and masquerade. Sometimes people would do things that reversed the normal social order in an intentionally crazy way—students would give mockingly fake lessons to their teachers, for example. In the past, people would even sometimes burn an effigy of Haman (similar to "Guy Fawkes Day" in Britain). (Source.)
The World Turned Upside Down
There are similar festivals in other countries. The Roman Empire celebrated a holiday called Saturnalia where slaves were served by their masters, instead of the other way around. In India, Hindus traditionally celebrate a holiday called "Holi," which celebrates another unexpected victory of good over evil and which involves throwing colored powder that helps cover up people's class differences for a day. And in Britain there was a day where the "Lord of Misrule" presided over a "Feast of Fools" close to Christmas—another anarchistic and fun-filled holiday.
These holidays are traditionally a good way of letting off steam, switching everything upside down helps people to relax enough to keep going when things are back to the way they were before. But they also implicitly admit that there could be a better way of doing things: the way the world is currently organized isn't final, isn't the only way it all could be.
Also, the title of the holiday "Purim" comes from the lot, or "Pur," Haman cast to try to determine the day the massacre would occur. As it was, the lot was turned against him. The day it landed on became the day when his plan was foiled (too bad for him, eh?).