The Bnei Yissaschar (Tishrei 8) discusses the holiness of Yom Kippur. He points out that when the Torah discusses the korbanos of Yom Kippur (Vayikra 16), it doesn't write the date telling us when to bring these korbanos! It doesn't state that these korbanos are for Yom Kippur! "Rather, the parashah tells us the avodah of the day, without telling us which day it is referring to, and then [after several pasukim] it mentions the date as if it was an afterthought (see Vaykira 16:29).
In contrast, when the Torah discusses all other yomim tovim, it first states the date, and then tells us the avodah of that day. But for Yom Kippur, it is the opposite! I think this is to reveal to us the holiness of the day...that we should know that Yom Kippur is a concealed, divine day... It is Olam HaBa. (We don't eat and drink on this day, and the Zohar tells us that this is because it is like Olam HaBa, where there is no eating or drinking)."
In other words, Yom Kippur is hardly mentioned because it is a day beyond time. It is a very exalted day, concealed entirely from this world.
The Bnei Yissaschar continues, "Also, the masechta that discusses Yom Kippur isn't called 'Yom Kippur' (as there are other masechtos that tell the name of the holiday, such as masechtos Shabbos, Rosh Hashanah, and Succah). It is called 'Yoma,' day. This too reveals the holiness of the day, that it comes from a concealed place, and it is proper to conceal it.
"This is the reason for the custom of anshei maaseh [G-d fearing Jews] that they don't say 'Yom Kippur.' Instead, when they mention the day, they call it, 'The Holy Day.' Understand this."
It states (Vayikra 16:2) הקודש אל עת בכל יבא ואל, "The [Kohen Gadol] should not come at all times into the Kodesh HaKedashim." The Kli Yakar explains that he may not enter on any day connected to time – עת. He may only go there on Yom Kippur, a day above time.
On this spiritual day, the Jewish nation becomes like the malachim. The Tur (606, quoting Pirkei d'Reb Eliezer) writes, "The Satan sees that there are no sins among the Jewish nation on Yom Kippur and says, 'Master of the world, You have a nation on earth that resembles the malachim in heaven. Just as malachim go barefoot, so do the Jewish people on Yom Kippur. Malachim do not have knees, and similarly, the Jewish nation stands erect throughout the entire day. Malachim are pure from all transgressions, as is the Jewish nation on Yom Kippur. Among the angels, there is peace, and likewise, there is peace among the Jewish nation, as they seek forgiveness from one another before this day.' Hakadosh Baruch Hu accepts the Satan's testimony and forgives their sins."
On Yom Kippur, when the Jewish nation is pure like the malachim, they shout out in public, ועד לעולם מלכותו כבוד שם ברוך. The Midrash (Devarim Rabba 2:36) states that when Moshe was in heaven, he heard the malachim praising Hakadosh Baruch Hu with these words. Throughout the year, we recite this praise silently. The Midrash expounds, 'It can be likened to someone who stole jewelry from the king's palace and gave it to his wife. He instructs her, "Do not wear the jewelry publicly, only at home." But on Yom Kippur, when we resemble angels, we boldly proclaim this praise aloud.'
The Gemara (Shabbos 129) teaches, "A person should sell the walls of his home to buy shoes." The mekubalim explain that the earth was cursed (due to Adam HaRishon's sin, see Bereishis 3:17); therefore, one should wear shoes to separate himself from the impurity of the earth. On Yom Kippur and in the Beis HaMikdash, however, the Yidden go barefoot. The Mishnas Chassidim explains that it is beneficial for us to go barefoot on Yom Kippur and in the Beis HaMikdash because this enables us to acquire the holiness that's there.
The gabbai of the Sar Shalom of Belz zt'l saw his Rebbe inhaling deeply on Yom Kippur. "Are you ok?" the gabbai asked. "Perhaps you need to eat?" The Sar Shalom replied, "I'm fine. I just wanted to inhale the holy air of Yom Kippur."
About Yom Kippur it states (Yoel 2:11), כי מאוד ונורא 'ה יום גדול, "For Hashem's day is great and very awesome." Indeed, we have seen that it is a very holy day. From this day, we can acquire holiness and closeness to Hashem that will be experienced and appreciated throughout the year.
