One of the most prominent aspects of the Avodas Yom HaKippurim in the Mikdash is the service of the sh'nei has'irim, the two goats. The halacha requires them to be identical in height and appearance (Yoma 6:1). A lottery was performed on them with one being designated as a korban laShem, its blood being sprinkled in the Holy of Holies, something done with no other korban other than the bull of the Kohein Gadol also offered on Yom Kippur. The second was designated as the s'air la'Azazeil to be thrown off a steep cliff which, in the language of the Mishna, "did not reach halfway [down] until it was turned into a pile of limbs" (ibid. 6:6).
This out of the ordinary service is clearly one of the chukim of the Torah, with no explicit reason given for it. However, many approaches have been taken attempting to uncover a glimpse into the Divine messages inherent within this service.[1] I have heard an approach whose source I do no not recall which seems to match the details of the mitzvah well.[2] This approach can serve as a central focus of what we attempt to accomplish on the "Shabbat Shabbaton".
G-d created Man originally pure without a tendency toward Evil (see Koheles 7:29). The Yeitzer Hara was external as represented by the Primeval Snake. When man sinned, the Evil Inclination became internalized. This led to a state of "tov v'ra", where good and evil where seemingly intermingled in the human mind. Confusion, lack of clarity, and indecision became the new reality for mankind. Only by studying and performing the Torah would mankind be able to rise beyond the confusion of this new reality. However, the ultimate plan of the Creator is to restore the original state of perfection which will occur in the Messianic era when the circumcision of the heart will occur (see Ramban to Nitzavim 30:6), meaning the elimination of the evil within each and every one of us.
However, even before that era, Yom Kippur gives us a glimpse of our real selves. The two goats similar in appearance both represent the same individual. Each of us has a "split-personality": the fundamental, true personality and the superimposed, fake persona infused into us with the entrance of the Yeitzer Hara. On this day, we separate the real from the fake, the fundamental from the artificial. The real personality, represented by the sa'ir laShem, created in the Image of G-d, is brought into the Holy of Holies, symbolizing Man's calling to cleave to G-d throughout his existence. The fake persona is dispatched and meets a violent end on a rocky mountain. This represents the end of Evil, the end of confusion, the end of indecision.
Yom Kippur is the day when we "take a break from the world", when we rest not only from labor, but we "rest" from most aspects of Olam HaZeh (see Rambam Hilchos Sh'visas Asor 1:5-6). The numerous drives and desires inherent in the world, when channeled properly, elevate us, and even make us higher than the angels who do not have the ability to elevate the physical. This occurs when we listen to our real personality. But the drives of the world also have the potential to, and often do, drive us away from G-d when we view these drives and desires as reality itself. This is a result of the fake persona within us. On Yom Kippur we rediscover who we really are.
This concept is further highlighted by a beautiful insight of the Maharal (Nesivos Olam, Nesiv Ha'Avoda). We recite the phrase "Baruch Sheim k'vod mal'chuso l'olam va'ed" silently during the whole year but aloud on Yom HaKippurim. The Midrash explains that Moshe Rabbeinu heard the angels reciting this verse and taught it to the Jews. But since it is an angelic declaration of Divine sovereignty, we recite it silently. Why then do we recite it at all if we are not angels? Maharal explains that we do so because there is part of us that is angelic; the soul, the core of who we really are, is constantly on the level of the angels capable of declaring this angelic form of acceptance of Mal'chus Shamayim. But this part of us is seemingly inaccessible to us, hidden as it were in the inner recesses of our existence. We recite "Baruch Sheim" silently the rest of the year because only the silent, hidden part of us is on that level. On Yom Kippur though, when the "soul emerges", we are capable of reciting this verse aloud. Yom Kippur shows us who we really are.
With this renewed awareness of the intense sanctity of the human personality and especially of the covenantal, Jewish people coupled with our repentance, may we achieve, with Divine mercy, forgiveness for our sins and the re-awakening of the central attitude necessary to face the "regular world" as we march one step closer to the era when evil will be eradicated forever.
[1] See Ramban, Rav Hirsch, and Rav Soloveitchik in 'Al HaTeshuva for various approaches.
[2]I would be indebted to a reader who can provide the source.