The Sixth month on the Scriptural calendar is the final month before the Fall Moadim start. (The last 4 Appointed times (Moadim) are the Fall Appointments that we have with YHVH ~ 'Fall' as in Yisrael's Fall season). This Sixth Month on the Scriptural calendar is also called Elul since Babylonian exile. The word "Elul" (aleph, lamed, vav, lamed), the after-captivity name of this month, forms the well- known acronym “Ani Ldodi Vdodi Li” which means "I am my beloved's and my beloved is mine". (Song of Songs 6:3). Elul normally corresponds on the Gregorian calendar with August/September.
Fall Moadim (Appointed times):
Yom Teruah (Feast of Trumpets or Day of the Awakening blast),
Yom HaKippurim, (Day of the coverings also known as Day of Atonement)
Sukkot (the 7 day Festival of Booths or Tabernacles)
And Shemeni Atzereth (the Eighth Day assembly that falls on the eighth day at the end of the seven days of Sukkot.) This Eighth Day Assembly (Shemeni Atzereth) is a one- day Appointment/Festival that speaks so beautifully of the "eighth day" (which at the same time is the First day of a new beginning) that will come after the Millennium (Millennium= the seventh thousandth year which gets portrayed beautifully by Sukkot) and will mark the new beginning of eternity.
Yom Teruah falls on the first day of the Seventh Scriptural month. (Normally it corresponds with somewhere during Sept or Oct on the Gregorian calendar) The Sixth Month (Elul) begins thus 29/30 days before Yom Teruah and 40 days before Yom Kippur. Jewish tradition treats this entire 40-day period as a time of spiritual preparation and renewal leading up to Yom Kippur.
Traditional services throughout the 29 or 30 days of this month of ELUL include blowing the shofar every day in the morning (the Jews don't blow it on Shabbat and also not on the last day of this Sixth Hebrew month, in anticipation for the start of Yom Teruah) as also readings from the Tehillim/Psalms. It is a good tradition and something that we can apply too to our personal prayer lives. (Not a commandment, so you don't have to do it.) It can be a blessing to read the entire Book of Tehillim/Psalms during this Sixth month though. If you read 4-5 average psalms a day, or 1-2 of the longer ones, you can make it through the entire book.
Some other interesting points
It was most likely (possibly) during the month of Elul that the ministry of Yochanan (John) the Immerser (Baptist) reached its peak. Possibly Yahshua was baptized on Elul 1 and he ended his 40 day fast on Yom HaKippurim. This is also the time that according to tradition, Moshe fasted 40 days the second time. It was on Yom HaKippurim (also known as Yom Kippur) that the Jubilee Year was announced every fifty years as stated in Vayiqra/Lev 25:8-10,
Traditional services throughout the 29 or 30 days of this month of ELUL include blowing the shofar every day in the morning (the Jews don't blow it on Shabbat and also not on the last day of this Sixth Hebrew month, in anticipation for the start of Yom Teruah) as also readings from the Tehillim/Psalms. It is a good tradition and something that we can apply too to our personal prayer lives. (Not a commandment, so you don't have to do it.) It can be a blessing to read the entire Book of Tehillim/Psalms during this Sixth month though. If you read 4-5 average psalms a day, or 1-2 of the longer ones, you can make it through the entire book.
Some other interesting points
It was most likely (possibly) during the month of Elul that the ministry of Yochanan (John) the Immerser (Baptist) reached its peak. Possibly Yahshua was baptized on Elul 1 and he ended his 40 day fast on Yom HaKippurim. This is also the time that according to tradition, Moshe fasted 40 days the second time. It was on Yom HaKippurim (also known as Yom Kippur) that the Jubilee Year was announced every fifty years as stated in Vayiqra/Lev 25:8-10,
"Count off seven sabbaths of years — seven times seven years — so that the seven sabbaths of years amount to a period of forty-nine years. Then have the trumpet sounded everywhere on the tenth day of the seventh month; on the Day of Atonement (Yom Kippur) sound the trumpet throughout your land. Consecrate the fiftieth year and proclaim liberty throughout the land to all its inhabitants. It shall be a jubilee for you; each one of you is to return to his family property and each to his own clan."
We read in Luke 4 what happened at the end of Yahshua's forty day fast (the fast possibly ended at Yom Kippur) :
"When the devil had completed every temptation, he departed from him until another time. Yahshua returned in the power of the Spirit into Galilee, and news about him spread through all the surrounding area. He taught in their synagogues, being esteemed by all. He came to Nazareth, where he had been brought up. He entered, as was his custom, into the synagogue on the Sabbath day, and stood up to read. The scroll of the prophet Isaiah was handed to him. He opened the scroll, and found the place where it was written, 'The Spirit of YHVH is on me, because he has anointed me to proclaim good news to the poor. He has sent me to heal the broken hearted, to proclaim release to the captives, recovering of sight to the blind, to deliver those who are crushed, and to proclaim the acceptable year of YHVH.' He closed the scroll, gave it back to the shammash, and sat down. The eyes of all in the synagogue were fastened on him. He began to tell them, 'Today, this Scripture has been fulfilled in your hearing.'" (Lk 4:13-21)
“The acceptable year of YHVH” speaks of a Jubilee year.
A Season of Repentance and Intimacy
Elul (the Sixtth Hebrew Month) is the month of preparation to meet the King and the Bridegroom. One of the interpretations of the after Babilonian exile Hebrew name ELUL like we mentioned above is that it stands for "Ani l'dodi, v'dodi li" "I am my beloved's, and my beloved is mine." (SS 6:3 NKJV) and it speaks of a time to seek intimacy with the Bridegroom to be sheltered in his love. Therefore Tehillim/Psalm 27 is traditionally read each morning.