Starting the day after Rosh Hodesh Elul, Sephardic Jews around the world wake up early to recite Selichot. Selichot consists of special prayers, psalms and supplications they are recited with a lot of different usually beautiful uplifting tunes with the exception of the viduy. The Selichot are recited every day until the end of the Yamim Nora'iim. The period between Rosh Hashanah and Yom Kippur is called Aseret Yeme Teshubah (The Ten Days of Repentance). During this period, we add extra prayers in the Tefillah and there are some extra supplications that we say in the Selichot.
According to the classic biblical commentator Rashi and others: Moshe (Moses) spent three forty-day periods on Mount Sinai starting the day after Shavuot: During the first he received the first set of Tablets, which he broke on the17th of Tammuz upon seeing the Golden Calf. During the second he pleaded with G-d to forgive the Jewish people for the sin of the Golden Calf. At the end of this period G-d reconciled with the Jewish people and told Moses to hew a second set of Tablets, so Moses went up for another 40 days. On the fortieth day of the third period (Yom Kippur) G-d fully pardoned the Jewish people, and Moses descended the mountain with the Ten Commandments inscribed on the second set of Tablets.
This third period, of good will and forgiveness, began on Rosh Chodesh Elul and concluded on Yom Kippur. Since then these forty days on the calendar have been designated as days of good will before G-d, and Yom Kippur as the Day of ultimate pardon and forgiveness. According to others when he came down on 17 of Tammuz he stayed down for 40 days and went back up on Rosh Hodesh Elul.
Based on this historical context Sepharadim start Selichot the day after Rosh Chodesh Elul and continue up to Yom Kippur. This is a very old custom mentioned by Rav Hai Gaon 939-1038ce and codified by the Shulchan Aruch OC 581:1 as a Sephardic minhag (custom). At Etz Ahaim selichot are held Sundays at 7.45 am and weekdays at 6.00 am. Everyone is welcome.