a) In the well-known, final mishna (and popular song version of the mishna) in Masechet Yoma, Rebbe Akiva asks:
לפני מי אתם מטהרין מי מטהר אתכם
“אביכם שבשמים, שנאמר “וזרקתי עליכם מים טהורים וטהרתם
ואומר “מקוה ישראל ה'”, מה מקוה מטהר את הטמאים, אף הקדוש ברוך הוא מטהר את ישראל
Yishayahu 59:2, states:
כִּי אִם עֲוֹנֹתֵיכֶם הָיוּ מַבְדִּלִים בֵּינֵכֶם לְבֵין אֱלֹהֵיכֶם
But your iniquities have separated between you and your G-d
During the year there is a separation between us and Hashem. Rav Schwartz attributes the lack of feeling closeness to Hashem that we may feel throughout the year, to (i) the sins we have committed, and (ii) being overly attached to physical needs and desires (even through attachment to physical things that are not prohibited per se).
On Yom Kippur, however, all the walls and separations come tumbling down: (i) The weight of our sins are alleviated because of the powerful nature of the day which is mechapeir us, spending our day adorned in angelic white garbs, immersed in davening; and (ii) our attachment to the physical is broken via the five inuyim (refraining from: eating/drinking, anointing, relations, washing, wearing leather shoes).
One of the main thrusts of Yom Kippur is certainly to atone for our sins and avoid punishment, but the real goal, he says, is for us to feel closer to Hashem. All the walls come down in a way that is unlike any other day of the year. Hashem fashioned us as his creations, so that we could strive to become closer to him. Late on Yom Kippur afternoon when the fast is getting to us, if we can think about all that we “can’t” do on Yom Kippur and all the davening we “have” to do on Yom Kippur as avenues to help us move closer to Hashem, then the grumbling in our stomach will hopefully subside and we’ll be able to make the most of this powerful day. The hope is that we take this special day on which the potential to feel close to Hashem is so magnified, and use that to launch ourselves into the pursuit of kirvas Hashem for the rest of the year.
b) A few years ago, Rav Yisroel Kaminetsky spoke on Kol Nidrei night about some reasons why we take out sifrei torah from the Aron Kodesh at the beginning of the Kol Nidrei service, but do not read from them – something we never do during the year. One answer he shared is the idea that we write the torah on the hide of an animal; a disgusting, dead carcass. The hide of an animal is so disgusting, yet we write the most beautiful thing in the world on it. We bring the torah around the shul before Yom Kippur, to drive home the idea that no matter how lowly or mired in sin we may feel, we can always turn ourselves into something magnificent.