It states in parashas Eikev (9:25) לפני ואתנפל יום ארבעים 'ה, "I fell before Hashem for forty days." Those were the days between rosh chodesh Elul until Yom Kippur (see Rashi Devarim 33:18). The Gr'a (Aderes Eliyahu, Ki Sisa 33:7) explains that during those forty days, Moshe didn't do anything other than tefillah. He fell before Hashem [and prayed for Bnei Yisrael]. Therefore, these forty days were established as days of prayer, and on Yom Kippur, להם ת"השי נתרצה, Hashem accepts their tefillos and teshuvah.
On Rosh Hashanah and Yom Kippur it will be determined what type of year it will be, and the tefillos in Elul sweeten the din and turns things to the better.
When Reb Yechezkel Levinstein zt'l was sick with cancer, r'l, he said that had he known in Elul that he would become sick that year, he would have ripped open the heavens in Elul and annulled the decree. The Chazon Ish zt'l would say that yiras Shamayim in our generation means emunah that everything that occurs, was destined on Rosh Hashanah. Therefore, let us invest in tefillah in Elul so that the upcoming year will be better than this one. That the upcoming year should be a year of wealth, health, peace, and prosperity. It should be the year of the coming of Moshiach, speedily in our days.
The mazal of Elul is besulah, which represents a bride before her chasunah. At the beginning of a chasunah, everyone is happy, but the chasan and kallah cry. They are happier than everyone else, but they understand the importance of davening at this special time because they know that their future lives depend on these tefillos. The same is true with Elul, mazal besulah. We trust that a good year is coming, and we are happy with Hashem's salvation, but we daven and cry because we know that tefillos will make it be so.
Reb Pinchas of Koritz zt'l discussed our apparent contradictory emotions on Rosh Hashanah. We are happy, as it states (Nehemiah 8:10, regarding Rosh Hashanah) ושתו משמנים אכלו 'ה חדות כי תעצבו אל ואתה ,לאדנינו היום קדוש כי ...ממתקים מעוזכם היא, 'Go, eat fat foods and drink sweet drinks...for the day is holy to Hashem. Do not be sad, for the joy...is your strength." On the other hand, there is the great fear of the judgment. Rebbe Pinchas Koritzer explains that it can be compared to a chasunah. Everyone is dancing and happy, but the people closest to the simcha may be crying. The same is true with Rosh Hashanah. It is a very happy day; we coronate Hashem as king; there is a lot to be happy about, but mixed in the joy is an element of fear because everything that will occur in the upcoming year depends on this day.
Reb Eliyahu Dessler zt'l said, "I am not a 'himmel mentch' (a person who has ruach hakodesh). I don't know what was decreed on Rosh Hashanah. But when the year passes by, I know exactly what was decreed on the last Rosh Hashanah. And the key to being found worthy in the judgment is to prepare for the judgment in Elul. As the Tur writes, "The more a person invests in tefillah in this month, it will be for his benefit."
The Rebbe Rashab of Lubavitz zt'l said, "Elul is the season for saying Tehillim." (He said this when he sent his gabbai to buy him a Tehillim in Elul.) Shaar HaMelech (1:2) encourages saying Tehillim every day in Elul after Shacharis. He writes, "I saw a good custom in many communities, and my parents also told me about this good custom. From rosh chodesh Elul until Yom Kippur, immediately after Shacharis, these communities say Tehillim with a crying and sweet voice. I decided to bring this good custom to our city. Tehillim is needed because our primary goal this month is to remove the mastinim (prosecuting malachim)... and nothing stops them as effectively as Tehillim. Tehillim is called mizmorim, which also means to shear because the Tehillim shears away all thorns [the prosecutors] ..."
Shaar HaMelech's Conclusion
"So, say Tehillim with kavanah and tears, and say the tefillah after each sefer of Tehillim. There should be ten people saying Tehillim, and they should also say the thirteen attributes of mercy at the end of the prayer. If you know of a place or city that doesn't know of this good custom, you should tell them about it so that every day of Elul we will be with the Tehillim. The Tehillim will be precious to Hashem as if we had studied the laws of negaim and ohalos, and the merit of Dovid HaMelech a'h will protect us, to receive a good judgment, for life and peace."
The Lion Has Roared
(Amos 3:6-8) יראה לא מי שאג אריה, "A lion has roared; who will not fear?" This pasuk alludes to Elul and the days of awe because אריה is roshei teivos for רבא הושענא ,כיפור יום ,השנה ראש אלול, days of teshuvah, hinting at the fear we have in those days. Someone asked Reb Chaim Kanievsky zt'l that if the pasuk alludes to Elul and the days of judgment, it should be in the present tense because the immense fear comes each year anew. Why does it state שאג אריה, "A lion roared," in the past tense? Reb Chaim zt'l replied that the pasuk is saying, "Think about what happened this year. You saw the tragedies, the problems. The lion has roared, r'l. This should inspire us to invest in tefillah."
Imagine the Elul before the Holocaust began. If people knew what to expect, they would have invested in Elul with all their hearts and souls. We never know what is approaching, but there are years of שאג אריה, great devastation, and we can save ourselves and avoid them with sincere tefillos in Elul.