(Based on Likkutei Torah p. 32 and the explanations of the Rebbe on the discourse)
1. Ani Ledodi Vedodi Li:
Its connection to Elul: The Abudarham writes that the above verse is the acronym for the word אלול, thus teaching us that the meaning behind this verse is the message of the month.
Its meaning: The term אני לדודי means that one is performing his Divine service to become closer to G-D. This is done by one arousing inner love and fear for G-d. This form of service is an אתערותא דלתתא [arousal from below] and is the Divine service required in Elul. The term ודודי לי refers to an אתערותא דלעילא, an arousal from above, from G-D, to draw down and reveal G-dliness below. This revelation takes place on Rosh Hashanah and Yom Kippur. Thus Elul is the aspect of אני לדודי while Rosh Hashanah is the aspect of ודודי לי.
The revelation of Rosh Hashanah: On Rosh Hashanah and Yom Kippur there is a revelation of G-d’s Kingship [מלכותו יתברך] which penetrates into a person [love and] fear of G-d for the entire year, and thus affects him to accept the yolk of Heaven. [The reason why this revelation of fear is needed and it’s not enough for a person to arouse it on his own is because] the love and fear of G-d that one has throughout the year cannot be aroused solely through one’s own efforts, rather it must be originally drawn into ones heart on Rosh Hashanah and commensurate to that revelation is one’s ability to arouse his love and fear of G-d throughout the year.
The preparation in Elul: Ones service of G-d in Elul is a preparation for drawing down this love and fear in Tishrei, which is drawn for ones entire year. Thus the אתערותא דלעילא in Tishrei is commensurate to ones אתערותא דלתתא done in Elul.
2. The revelation of the thirteen attributes of mercy:
Its connection to the month of Elul: It says in Mishnas Chassidim and Peri Eitz Chaim that in the month of Elul G-D reveals His thirteen attributes of mercy.
Gives one potential to do service needed in Elul: Although the month of Elul, as explained above, is emphasizing the service of man towards G-D, which then elicits a revelation from above in the month of Tishrei, nevertheless being that every service done below (אתעדל“ת) must have its potential elicited from above (אתעדל“ע), therefore in this month G-D reveals His thirteen attributes of mercy towards man in order to give him the potential to do his service of the month. Thus even those people which are in a very distanced state from spirituality and G-D, now are given the potential to make amends of their wrongdoing and reunite with G-D.
Represents a loving unity with G-d: The thirteen attributes of mercy represent not only a revelation of G-d’s will to forgive even the most severe sins, but mainly a revelation of the most internal level of His radiance termed פנמיות אא“ס. This radiance is represented by the first of the 13 attributes, the name א–ל. So too each and every Jew also has an aspect of שם א–ל within him, this being his G-dly spark which enlivens his G-dly soul. This is the reason that we are called י–שר–א–ל, as the name represents that our level of א–ל is constantly within us and retains its holiness even after its been descended by man into impurity due to his sins. Thus by one revealing his level of א–ל in the month of Elul he effects a unity of his most inner self with the highest level of G-dliness.
3. The Parable of the “King In The Field”:
The above mentioned points regarding the month of Elul and its affect on the revelations of the month of Tishrei is explained by a parable. When a king sits at his throne only a very select few may enter into his inner chambers and bask in the king’s presence. However when the king decides to descend from his throne and visit the fields of his kingdom, every man and woman is then given the chance to greet the king despite them being common folk. All that is required of them to do is to leave their city and enter the field to greet the king. The king then shows his subjects פנים מאירות ופנים שוחקות [a shining face], and when he returns to his throne all those which came to greet him are given permission to follow. This parable is an exact analysis of the events of the month of Elul and of Tishrei.
The following points can be learnt from the parable:
- The King Descends To The field-A revelation of the thirteen attributes of mercy: In Elul G-d reveals His thirteen attributes of mercy to all. This corresponds to the King descending from his throne and giving ability to all his subjects to greet him. Just like when in the field the king does not come with all of his external glory and majesty but rather in a simplistic way, which does not arouse awe and trepidation towards his subjects but rather only gives his subjects the ability to come greet him, so too this revelation of the thirteen attributes of mercy does not arouse one to fear or accept G-d’s Kingship, and rather it simply gives him the potential and will to accept it. Thus this part of the parable explains that despite their being a great revelation in Elul it is still termed a month of אתדל“ת, of mans service of G-d, as this revelation does not arouse him to do the service and thus the arousal must be done by mans own initiative.
- Going out to the field-Kabalas Ol: Going out in the fields in the parable represents the people accepting the yolk of Kingship [Kabalas Ol Malchus Shamayim], showing that they truly feel his power and awesomeness and therefore they go out to greet him. Similarly during the month of Elul the main service is the accepting the yolk of heaven which in is the beginning and main aspect of Teshuva.
- Why the month of Elul is not a Holiday: The parable answers two potential questions regarding the revelation of the month of Elul. If Elul has the revelation of the thirteen attributes of mercy, then why is it that it is not termed a holiday which is forbidden in doing mundane matters like is the case with other holidays which have an even lower revelation of G-dliness? Furthermore, on Yom Kippur there is also a revelation of the thirteen attributes of mercy, so what is the difference between Elul and Yom Kippur? The above is answered by the parables statement that the king is entering into the field. Meaning the king is descending to the level of his people, even towards those of a lower occupation such as those who work in the fields. This represents that in Elul G-d reveals His thirteen attributes of mercy to all, even to those who are involved in the mundane aspects of the world. It is for this reason that Elul remains a typical month that is allowed in mundane activity, and is not a holiday which forbids work, as this is the exact emphasis of the revelation. Furthermore, there is an advantage in the “work of the field” over even those that are occupied in constant Torah learning, as through using the matters of the physical world to serve G-d and see the providence and light of G-d in all one’s mundane activities he elevates those matters towards G-d thus fulfilling the Divine purpose of creation which was to make an abode for G-d within the physical world. It is also understood the difference between Yom Kippur and Elul, as by Elul the thirteen attributes descends towards our level, while by Yom Kippur we are elevated to its level, as is seen from fact that we try to emulate angels and refrain from all physical acts such as eating and drinking etc.
- Once greeted the King then shows his subjects a shining countenance-An arousal of delight for G-dliness and desire to cleave to Him: Once one has done his service of acceptance of G-d as his King and Lord he then receives the full revelation of the 13 attributes of mercy which, as already explained above, is an arousal of one’s most inner level of his G-dly soul. This arouses one to have a strong desire to cleave to G-d and thus repent any wrongdoing from the most inner depths of his soul.
 Sefer Hamamarim Melukat-Elul p. 224 [Mamar Parshas Shoftim1972]; Sefer Hamamarim 1940 p. 166
 Vetzrauch Iyun as above the Alter Rebbe says that the service of Elul is to arouse ones love and fear? One must thus conclude that although this is also required in Elul, the main Avoda of Elul is Kabalas Ol and fear of Heaven.