Today, the 7th of Adar, is both the birthday and yartzeit of Moshe Rebbenu (Moshe our teacher), the man who brought us out of Egypt, received the Torah, and who advocated on our behalf in front of Hashem.
Moshe was born in Egypt on the 7th of Adar of the year 2368 from creation (1393 BCE) and passed away on his 120th birthday -- Adar 7, 2488 (1273 BCE). The Rambam (Maimonides) calls him "the most perfect human being", and our sages said that "the Divine presence spoke from his throat." Yet he is also called "the most humble man on earth." He is a man who spoke to G-d, yet a man who was very much of this world, working as a shepherd for 60 years before becoming the greatest of prophets, and even marrying a convert, namely Tzipporah, the daughter of the pagan priest Jethro.
The fact that Moshe passed on in Adar was one of the reasons that Haman chose this month as the month to kill the Jews. He believed that the month that Moshe died would be an unlucky month for the Jews. However, he misunderstood what the death of Moshe, and the death of a tzaddik, really means. In the book of Shemot we learn that G-d told Moshe that "I shall complete the number of your days", meaning that Moshe would pass away on his birthday after 120 years. Thus Moshe did not have his life cut short; rather his life was completed. And having a complete life is no tragedy at all.
Oddly, no special customs are observed on this day, except for one: On this day the Chevra Kaddishas (Jewish Buriel Societies) hold their annual get-togethers and feasts, based on the tradition that G-d buried Moshe Rebbenu himself, thus giving them a rest from their labors.