The last of four special Shabbatot before Passover, Shabbat Hahodesh falls on the Shabbat before the month of Nisan begins, or else - as this year - it falls on the first day of Nisan when that day is Shabbat.
The special maftir aliyah reading comes from Shemot 12:1-20, from Parashat Bo, and it describes the night of the first Passover, including eating the Pesah lamb sacrifice, roasted not boiled, with unleavened bread and bitter herbs, and painting the blood of the sacrificed lamb on the doorposts of Israelite houses so that the Angel of Death would pass them over. They were told to eat this combination of foods with loins girded, sandals on their feet, and their staff in hand, hurriedly, after the painting was done, and before they were to burn the leftovers and then bear witness to the slaying of the first born of the Egyptians. Reading this portion is a blatant reminder that we should be preparing for Pesah!
There is also a special haftarah for this Shabbat. It describes the sacrifices the Israelites are to bring on the first of Nisan, on Passover, and on other festivals in the (future) Temple.
On the first day of Nisan, God presented the first commandment with details of celebrating the New Moon (Kiddush hahodesh, sanctification of the month). Thus Nisan became the first month of the Jewish year (although there are four different new years that we may celebrate). (Mishnah Rosh Hashanah 1:1.)
Okay, before you ask me, the three other new years are Rosh Hashanah (1 Tishrei), Tu Bishvat (15 Shevat, the new year of the trees), and 1 Elul for the tithing of the cattle - bovine were taxed by what year they were born, and all born after 1 Elul were considered born in the same year.