Many of the Rebbe's sichos
explaining the nature of the month of Elul center around the explanation of the rashei teivos
(initial letters) of the verse in Shir HaShirim,
(Ani LeDodi VeDodi li
-- "I am for my Beloved, and my Beloved is for me"). These letters spell Elul. This verse indicates the relationship between HaShem
and the Jewish People throughout the year, and particularly during the month of Elul -- a month of teshuvah
on our part, and a month of compassion and forgiveness on the part of HaShem
The Rebbe also points out that the final letters of each word in the verse ani ledodi vedodi li are all yuds, each of which has a numerical value of ten. Thus together, the four yuds add up to forty. What is the significance of this number? That there are forty days from the first day of Elul until Yom Kippur. This indicates that the central concepts of the month of Elul do not end at the end of Elul, but extend to Yom Kippur. In other words, the first ten days of Tishrei also fall into this category of Elul. After Yom Kippur, however, the mood changes.
From the beginning of Elul until Yom Kippur is a serious time of year -- the Yamim Noraim, or the "Days of Awe." After Yom Kippur, we start with preparations for Sukkos, when the joyful aspect of simchah prevails. Thus, the relationship which we have with HaShem from the first day of the month of Elul ends with Neilah, the final prayer of Yom Kippur. During Neilah (which literally means "closing" or "locking") the gates are closed. A chapter has closed, and we open a new chapter where HaShem relates to the Jewish people in a different way.
The forty days from Rosh Chodesh Elul to Yom Kippur are days of rachamim -- compassion. It was during this time that Moshe Rabbeinu communed with HaShem for forty days in order to obtain forgiveness for the Jewish People after the sin of the Golden Calf. On Yom Kippur he was given the second set of stone tablets on which the Ten Commandments were written. Therefore, these are the days that have always remained days of rachamim (compassion) and selichah (forgiveness).
Once the forty days are over and we have finished this era, we start a new period, which is the days of joy of Sukkos. This begins right after Yom Kippur, because we start preparing for Sukkos: we start building the sukkah, and start getting into the mood of Sukkos.
In keeping with the spirit of this month, then, the Rebbe spoke many times about helping people get what they need for Yom-Tov. Tishrei can be an expensive month, with all the food, clothing, a sukkah, the arbaah minim (Four Species) required for Sukkos, etc. Paradoxically, before Tishrei, you shouldn't think only about your own spiritual preparations. You also have to think about gashmiyus (material needs) -- other people's gashmiyus. You have to worry about your teshuvah (repentance), but for other people, you have to worry about their material needs. You're not obligated to go around saying, "Repent! Do teshuvah! Did you daven enough? Did you learn enough?" That is for you to take care of for yourself. For the other person you have to ask, "Does he have chickens, does he have meat, does he have challah?" Because, as the Rebbe has repeated on numerous occasions -- the gashmiyus of another Jew, for you, is ruchniyus (spirituality). In other words, when you take care of your own gashmiyus, it's merely gashmiyus, but when you worry about somebody else's gashmiyus, it's ruchniyus. Therefore, on erev Rosh HaShanah we have to worry about other Jews; we have to make sure they have their provisions.
I would like to give a practical suggestion to anyone who has not managed to really put energy into the direction of giving tzedakah (charity) to help people get their needs for Yom-Tov. I know that in Yerushalayim there is an organization called Collel Chabad, that provides meals for people who are elderly or who don't have families. This is one place you can give your tzedakah. There are also many other places that provide food. Try to find an organization that is involved in giving money, food packages, etc., to poor people. Put your tzedakah into this area now. While it is important to give money for Torah and yeshivos, now the important consideration is that Jews should be happy, and you can only be happy if your stomach is not groaning for food. By the eve of the festival, people should have their needs; people should not have to worry, "How am I going to buy meat? Maybe we'll just eat cottage cheese this Yom-Tov, because we cannot afford meat." There is a story of a certain rav to whom one of the members of his community came on the eve of a festival with a question: Is it permitted to make Kiddush on milk? The rav thought for several minutes and then replied that this was permitted. As soon as the person had left, the Rav told his wife to immediately send over wine and meat and other goodies to that family. "Why meat?" she asked, "He apparently lacks only wine!" "If he intended to make Kiddush on milk," the rav replied, "it is obvious that there was no meat for the meal either, for one cannot have milk and meat at the same meal!"
On Yom-Tov everyone should be happy. This is what should concern us in Elul. This is the best preparation for Yom-Tov.