Taken from Pachad Yitzchak by Rav Yitzchak Hutner

To answer this question we must first look at a few other issues and raise a few more questions. Everyone knows that the time of year between Rosh HaShana and Yom HaKippurim is a time when Hashem is close to man and thus that it is a prime time to seize every opportunity to bring oneself close to Hashem (See Isaiah 55:6 - "Seek Hashem when He is to be found, call Him when He is close"). While this can be done in many ways, the best way to do so is through prayer. One of the principles of teshuva itself is that one pray for success in doing teshuva, and Rabbeinu Yona includes this as his fifth principle of teshuva. As these are days that are specifically designated to be days for teshuva, prayer that includes within itself a plea for teshuva and forgiveness as it were works "double-time" in achieving this goal. As we will see, there is a deeper understanding to be had about the role of prayer that has teshuva as its foundation.

With regard to prayer during this time, the selichot that are said from before Rosh HaShana until Yom HaKippurim are somewhat strange in their arrangement. Every days' selichot include Ashrei, kaddish, and tachanun, a combination that we do not see in any other supplicative prayers for any other requests (i.e. livelihood). Why the difference?

Our answer begins with a look into the crucial part of the selichot, namely the thirteen attributes of mercy that are the core of all selichot. The first two attributes are the name "Hashem," and the gemara relates that the first one refers to an attribute of Hashem towards a person before he sins, while the second refers to an attribute of Hashem to a person after he sins and does teshuva. However, we are told as well that the last attribute, that of "vi-nakeh," literally that Hashem will cleanse, is the attribute that refers to teshuva! Which one is it? The Maharal of Prague answers that one who repents for all of his sins deals, as it were, with the attribute of the second "Hashem," while one who repents for only some of his sins deals with the attribute of "vi-nakeh." What does this mean? Why are two attributes needed to describe how Hashem relates to a person who has done repentance, either total or partial?

To understand, we must look at what exactly the term "Hashem" means. The term "Hashem" contains within it the essence of the true power of teshuva. Teshuva is not defined by a word that has a definition, but rather by the undefinable word "Hashem," a word that relates to Hashem alone (unlike other names of God which are used in non-divine context; for example, "Elohim" can refer to a judge as well as to God [see Shemot 22]). The reason for this is that teshuva is not a power that exists anywhere in the natural order of the world, but rather it is something that Hashem Himself creates anew. The simple meaning of the name "Hashem" is the ability of Hashem to constantly create and renew the world, and thus the use of this term here characterizes teshuva as something that appears in the world ex nihilo (yeish me-ayin). The power of the original creation of the world, signified by the first "Hashem," lasts only until man sins. At the very point of sin, at that moment of spiritual destruction, Hashem creates a new world, the world of teshuva. It is in this world that Hashem's attribute of "erech apayim" - His being long-suffering, appears, as this attribute signifies Hashem's waiting for a person to repent. Without the possibility of teshuva, which occurs only in this "new" world, there is no reason for the attribute of "erech apayim" to exist.

Given the creation of this new world, we can understand the point of the Maharal regarding the two attributes that deal with repentance. The attribute of "Hashem" that comes after one sins and repents applies to a situation similar to that of the first "Hashem." The first "Hashem" deals with a world without sin, a world before any wrongdoing has occurred. To parallel this, the second "Hashem" must also deal with a sin-free world, namely a world wherein a person has repented for all of his sins. Thus, how does one get from sin to repentance? How does he chip away at his sins until he reaches a stage where he has repented for all of them? This is accomplished by relating to the attribute of "vi-nakeh," which deals with those who have not yet repented for all of their sins.

We can now begin understanding the special role of prayer as it relates to teshuva. At the Red Sea, Hashem told Moshe not to cry to Him, as the splitting of the sea depended on Hashem alone, not on human prayers. Why is this so? The gemara tells us that the splitting of the Red Sea was an event whose occurrence was worked into creation from the start, and things that are inherent in the beginning of creation are not subject to change as a result of human prayer. So too is the case with teshuva, which becomes part of its own creation, and thus does not fall under the category of regular human prayer.

This point is brought out by the gemara in Rosh HaShana, which states that Hashem, as it were, wrapped Himself in a tallit and taught Moshe the thirteen attributes. However, we already know about the obligation to pray from another source, so why was this particular prayer not included there? The answer is exactly what we have been saying. This prayer was taught to Moshe in the wake of the sin of the Golden Calf, and thus it was related specifically to teshuva and the world of teshuva. As a result, it had to be taught in a special revelation to Moshe. As the gemara states: Had the verse (teaching this prayer) not be written, we would not be able to say it. To bring this back to one of our original questions, we can now understand better why the format of selichot differs from that of any other supplicative prayer. We are not merely asking for food or livelihood, but rather we are asking for something that exists in a different world, and therefore we need to construct a prayer that can relate to that world.

This strange term opens up a path for us to understand the real point of Yom HaKippurim. At its heart, this is not merely a day of repentance, but it is the day when the Jews were "remarried" to Hashem through the giving of the second set of tablets at Har Sinai. Between the giving of the two sets of tablets occurred the sin of the Golden Calf and the repentance of the Jews, and thus the two sets of tablets were given, as it were, to two separate worlds. As such, each world received a separate commandment with regard to prayer, and each world has a separate verse regarding the giving of the Torah. The Torah was first given in the context of a world before sin; it was given the second time through repentance from sin. Thus we see that Shavuot and Yom HaKippurim, which commemorate the two givings of the Torah, share opposite sides of a unique aspect in the context of all of the holidays. In discussing whether or not the holidays should be dedicated completely to Hashem or if part of the day should be enjoyed by man for his own benefit, all opinions agree that on Shavuot there must be some aspect of "lachem" - for yourself. Why is this so? Because this is the day on which the Torah was given over to man ("lo bashamayim hee" - the Torah is no longer subject to Divine jurisdiction, but rather to human judgement; see Bava Metzia 59b). By contrast, Yom HaKippurim is the day that is entirely devoted to Hashem, devoid of any "lachem." Our abstaining from food and drink on this day does not stem from a desire to physically torture oneself, but rather from the fact that a fast day premised entirely on teshuva is a day that focuses solely of the spiritual side of man, and not on the physical.

Returning now to our point of departure. Recall the opinion of Rabbeinu Yona, that the specific commandment of teshuva on Yom HaKippurim is focused on tahara, spiritual cleansing. This focus can now clearly be seen to flow from what the teshuva of this day is. This day has its own giving of the Torah and its own teshuva, and that teshuva relates directly to that second giving of the Torah. The entire nature of the day stems from this combination, and together they create a day that has only one focus - Hashem. The point of connection between the two is the passage from the world of the first "Hashem" into the world of the second "Hashem," a passage that requires one to cleanse himself of all of his sins, to perform a total self-purification.