On the last day of Av of the year 2448 from creation (1313 BCE), Moses carved, by G-d's command, two stone tablets -- each a cube measuring 6x6x3 tefachim (a tefach, "handbreadth", is approximately 3.2 inches) -- to replace the two divinely-made tablets, on which G-d had inscribed the Ten Commandments, which Moses had smashed 42 days earlier upon witnessing Israel's worship of the Golden Calf.
Today is the first of the two days of Rosh Chodesh (“Head of the Month”) for the month of Elul (when a month has 30 days, both the last day of the month and the first day of the following month serve as the following month’s Rosh Chodesh).
Special portions are added to the daily prayers: Hallel (Psalms 113-118) is recited—in its “partial” form—following the Shacharit morning prayer, and the Yaaleh Veyavo prayer is added to the Amidah and to Grace After Meals; the additional Musaf prayer is said (when Rosh Chodesh is Shabbat, special additions are made to the Shabbat Musaf). Tachanun (confession of sins) and similar prayers are omitted.
Many have the custom to mark Rosh Chodesh with a festive meal and reduced work activity. The latter custom is prevalent amongst women, who have a special affinity with Rosh Chodesh—the month being the feminine aspect of the Jewish calendar.
Beginning today, the psalm L'David Hashem Ori (Psalm 27) is recited at the end of the morning and afternoon prayers. This special addition is recited throughout the month of Elul and the High Holiday season, until Hoshanah Rabbah (Tishrei 21) -- a total of 50 days.
Links: Psalm 27, The High Holiday Anthem