In the Book of Esther, a distinction is made between Jews who live in a walled city, and those who live in unwalled cities.  The rule in the Mishna (Megillah 1:1) is that all walled cities since the days of Joshua were to celebrate Purim on the fifteenth day of the month of Adar.  All other cities were to celebrate the holiday on the fourteenth day of Adar.  Since Jerusalem is a walled city it celebrates Purim on the fifteenth.

In leap years, such as this one, there is an extra month of Adar (Adar 1, Adar 2) Purim is always celebrated during the second Adar.