The day before Purim is "Ta'anit Esther" (the Fast of Esther). Observant Jews fast on this day in remembrance of Esther's request of the Jews of the city of Shushan to fast for her before she went before the king.
Jews celebrate Purim by dressing up in costumes. Traditionally, Jews wore costumes of Queen Esther and her uncle, Mordecai, but today anything goes--from clowns to Spiderman to Spanish dancers. Purim parties are festive events with drinking, music, dancing, etc. One custom is to get so drunk that you can't tell the difference between the evil Haman and the righteous Mordecai.
On Purim, it is traditional to send "mishloah manot"--"goody bags" consisting of cookies and candies to friends and relatives. We eat "Hamantashen", triangular cookies usually filled with dates or poppy seeds.
Read the Story of Purim!