Reference for material: http://www.hebcal.com/holidays/rosh-chodesh-elul
Beginning of new Hebrew month of Elul. Elul is the 6th month of the Hebrew year. Corresponds to August or September on the Gregorian calendar.
The following is a text from: http://www.chabad.org/holidays/JewishNewYear/template_cdo/aid/293704/ jewish/Elul-Observances-in-a-Nutshell.htm
As the last month of the Jewish year, Elul is traditionally a time of introspection and stocktaking—a time to review one’s deeds and spiritual progress over the past year, and prepare for the upcoming “Days of Awe” of Rosh Hashanah and Yom Kippur. As the month of divine mercy and forgiveness, Elul is a most opportune time for teshuvah (“return” to G‑d), prayer, charity, and increased ahavat Yisrael (love for a fellow Jew), in the quest for self-improvement and coming closer to G‑d.
Chassidic master Rabbi Schneur Zalman of Liadi likens the month of Elul to a time when “the king is in the field” and, in contrast to when he is in the royal palace, “everyone who so desires is permitted to meet him, and he receives them all with a cheerful countenance, showing a smiling face to them all.”
The following are some of the basic customs and practices for the month of Elul: Each day of the month of Elul (except for Shabbat and the last day of Elul), we sound the shofar (ram’s horn) as a call to repentance. When writing a letter or meeting one another, we bless one another by including the greeting Ketivah vachatimah tovah—which roughly translates as “May you be inscribed and sealed for a good year.” Chapter 27 of the Book of Psalms is added to the daily prayers, in the morning and afternoon. The Baal Shem Tov instituted the custom of reciting three additional chapters of Psalms each day, from the first of Elul until Yom Kippur. (On Yom Kippur the remaining 36 chapters are recited, thereby completing the entire book of Psalms.) Elul is a good time to have one’s tefillin and mezuzot checked by an accredited scribe, to ensure that they are in good condition and fit for use.
During the last week of Elul, in the days leading up to Rosh Hashanah, the Selichot prayers are recited. On the first night they are recited at midnight; on the following days, in the early morning.