Death of King Nebuchadnezzar, the Babylonian emperor who conquered Jerusalem and destroyed the first Holy Temple 26 years earlier, died on the 25th of Adar of the year 3364 from creation. (Jeremiah 52:31)

Rebbetzin Chaya Mushkah Schneerson (1901-1988) of righteous memory, wife of the Lubavitcher Rebbe of righteous memory, was born on Shabbat, the 25th of Adar, in Babinovich, a town near the Russian city of Lubavitch, in the year 5661 from creation (1901). In an address delivered on the 25 of Adar of 1988 (the Rebbetzin's 87th birthday, and about a month after her passing), the Rebbe initiated an international birthday campaign, urging people to celebrate their birthdays and utilize the day as a time of introspection and making resolutions involving an increase in good deeds.

Links:
An on-line biography of the Rebbetzin
On the Jewish Birthday and the birthday customs

On the Shabbat that falls on or before the 1st of Nissan, a special reading called "Hachodesh" (Exodus 12:1-20) is added to the regular Shabbat Torah reading. Hachodesh recounts G-d's historic communication to Moses in Egypt on the 1st of Nissan (2 weeks before the Exodus) regarding the Jewish calendar, the month of Nissan and the Passover offering.

Links: Parshat Hachodesh with Commentary
From the teachings of the Chassidic masters on Hachodesh
About the Jewish calendar and the Passover offering

This Shabbat is Shabbat Mevarchim ("the Shabbat that blesses" the new month): a special prayer is recited blessing the Rosh Chodesh ("Head of the Month") of upcoming month of Nissan, which falls on Thursday of next week.

Prior to the blessing, we announce the precise time of the molad, the "birth" of the new moon. Click here for molad times.

It is a Chabad custom to recite the entire book of Psalms before morning prayers, and to conduct farbrengens (chassidic gatherings) in the course of the Shabbat.

Links: On the Significance of Shabbat Mevarchim; Tehillim (the Book of Psalms); The Farbrengen