The Mishnah in the fourth chapter of Megilah (29a) teaches that during the month of Adar we insert four special Torah readings. We will try to understand what and why those particular readings are read on those particular Shabatot.
The first of these readings is known as Parashat Shekalim. We read this parasha to commemorate the collecting of the half shekel from all Jewish adults which was then used to buy animals for public offerings (Korbanot Tzibur). This collection, we learn in the Mishna in Masechet Shekalim (2a), took place during the month of Adar since every Nisan marked a new year in the funding of public sacrifices. The Mishna teaches that on the first of Adar a proclamation would go out to remind the public of their duty to contribute the half shekel. In commemoration of this proclamation we read in the Torah on the Shabbat which is either the first of Adar or the one that proceeds the first of Adar. In the Gemara (Megilah 29b) we find a debate between Rav and Shemuel as to what should be read for Parashat Shekalim. Rav is of the opinion that we read the parasha of the Tamid sacrifice while Shemuel states we read the opening parasha of Ki Tisa. Shemuel’s opinion seems clear. Since the idea of collecting the half shekel is stated in Parashat Ki Tisa it is the obvious section to read. Rav on the other hand is of the opinion that since the purpose of the half shekel is to acquire animals for the Korbanot Hatzibur we should read the section of the daily public offering to remind us for what purpose the half shekel was collected.
On the Shabat proceeding Purim we read Parshat Zachor. (See Megilah 30a for an interesting debate as to when Parashat Zachor is read on years Purim comes out on Friday. We here wrote the time according to the accepted halachic ruling.) Zachor is the name for the section in Devarim (25/17-19) that commands us to retell what Amalek did to the Jewish people just after they left Egypt and which commands us to wipe out any remnant of that nation. The retelling of what was done by Amalek is considered a biblical mitzvah that should be performed at least once a year. At the time of Mordechai and Estherit was established that this mitzvah be performed before Purim since tradition has it that Haman was a descendant of Amalek and the miracle of Purim is a form of fulfillment of the destruction of Amalek.
The Shulchan Aruch (OC 685/7) writes that since the reading of Parshat Zachor is considered to be a fulfillment of a biblical mitzvah every person should make the effort to hear the reading in a Minyan. The Terumat Hadeshen states that if one is faced with the choice of hearing a public reading of Zachor or the Megilah on Purim the reading of Zachor should be preferred since the Megilah may be read by the individual as well. The Magen Avraham(OC 685) counters that since one could fulfill both the mitzvah of Zachor and the reading of the Megilah on Purim, when we read the story of Amalek’s attack,(Shemot 17/8-16) it is preferable to be in a Beit Knesset on Purim then on the Shabat of Parashat Zachor. Many of the later halachists (See Mishna Berurah 685/16 and Aruch Hashulchan Oc 685/5) argue with the Magen Avraham, stating that the reading on Purim from Shemot does not fulfill the halachic requirement for Zachor. The reasons suggested are that the story in Shemot is not in the form of a command and lacks the commandment to destroy Amalek.
The third special reading is that of Parshat Parah. In this reading we read the section in Bamidbar which tells of the preparation and use of the ashes of the Red Heifer. Being every Jew is expected to partake in the eating of the Korban Pesach, to do so one must be pure of any impurity brought about by contact with the dead. Since the Ashes of the Red Heifer were needed to purify people from such impurity, this reading is read after Purim and before Pesach.
Finally, on the last Shabat of Adar or if Rosh Chodesh Nisan comes out on Shabat then on that Shabat, we read the section known as Parshat Hachodesh. This is the section in Shemot (12/ 1) which reads “Hachodesh haze lachem rosh chodashim” in which we read of the commandment given to the Jewish people to prepare the Korban Pesach in Egypt, which is later to be commemorated with a yearly sacrifice on Pesach.
It should be noted that on a leap year these readings are read during the second Adar since they relate to preparations for Purim, Nisan or Pesach, all of which relate to the second Adar.