The Sages instituted four special Torah readings on four different Shabbats during the Purim season. These readings are read as the Maftir portion in the synagogue on Shabbat morning, immediately following the weekly parsha.
1. PARSHAT SHEKALIM
Exodus 30:11-16 is read in commemoration of the Half Shekel which every Jew brought during the month of Adar, to pay for the public offerings in the Holy Temple.
This portion is read on the Shabbat preceding Rosh Chodesh Adar (or Adar II in a leap year). If Rosh Chodesh falls on Shabbat itself, then that Shabbat is Parshat Shekalim.
What is the connection between the Half Shekel and Purim? When Haman proposed to Achashverosh the annihilation of the Jews, he offered to pay 10,000 "kikars" for the right to do so (Esther 3:9). Since one kikar equals 3,000 shekels, Haman was in fact putting a price tag of 30 million shekels on the Jews.
Since there are 600,000 main souls in the Jewish nation (see Numbers 2:32), and 50 shekels is the donation value of an adult male (as specified in Leviticus 27:3), this amount multiplied times 600,000 souls equals 30 million.
2. PARSHAT ZACHOR
The Shabbat immediately preceding Purim is called Shabbat Zachor. The portion of Amalek (Deut. 25:17-19) is read, since Haman was a descendant of Agog, King of Amalek.
One should be very careful to listen to all the words, since most halachic authorities consider it a Torah-level mitzvah to hear this portion once each year.
Zachor means to remember, and the Torah commands us to "remember what Amalek did to you on your way out of Egypt" (Deut. 25:17). The Sages explain that the definition of "remembering" is to speak the matter aloud at least once a year.
It is the widespread custom for women to attend synagogue and hear the reading.
If one accidentally missed Parshat Zachor, the obligation may be fulfilled by listening to the Torah reading on Purim itself, or to the weekly reading of Parshat Ki Tetzei(and according to many authorities, Parshat Beshalach as well).
You will notice that the reader repeats the word zaicher and zecher in the last verse, since there are two different opinions as to how that word is pronounced. This stresses the importance of hearing every word correctly.
3. PARSHAT PARAH
Parshat Parah (Numbers 19:1-22) is read on the Shabbat following Purim. These verses deal with the Red Heifer used in the spiritual purification process at the time of the Holy Temple. This issue is important at this season of the year, since in looking forward to Passover, every Jew is careful to maintain spiritual purity in order to partake in the holiday offerings.
Many authorities regard this reading as a Torah precept.
4. SHABBAT HACHODESH
Finally, on the Shabbat preceding Rosh Chodesh Nissan, we read the special Maftir from Exodus 12:1-20. These verses contain the commandment to make Nissan the head of all months. This was the first mitzvah given to the Jewish people while still in Egypt.
By declaring the new month, the Jewish people have the ability and responsibility to sanctify life and the passage of time.