Megillah, Chapter One, Mishnah Three
When Jews adjust the lunar calendar to keep it in sync with the solar calendar, they add a second month of Adar, the month during which Purim falls. The rabbis hold that Purim should be observed during the second Adar. Today because our calendar is fixed this is quite simple. Ahead of time we know which year will have a second Adar. In mishnaic times this was more difficult because the calendar had not yet been fixed. Our mishnah addresses this problem.
1) If they read the Megillah during the first Adar and the year was intercalated (a month was added), it is read again in the second Adar.
2) There is no difference between the first Adar and the second Adar except the reading of the Megillah and the giving of gifts to the poor.
Section one: If they read the Megillah during the first Adar and then the court decided to add a month to the year, they must read it again during the second Adar.
Section two: The only difference with regard to Purim between the first month of Adar and the second is that the Megillah is read and gifts are given to the poor during the second month and not during the first month. However, when it comes to the prohibition of fasting and mourning, it is forbidden to fast on the fourteenth and fifteenth of both months.
It is unclear from our mishnah whether the other two obligations for Purim, giving portions of food to friends and having a festive meal, are done both times or not. It seems to me that it would make little sense for these customs to be performed during the first Adar at a time when the Megillah is not being read.