Regarding the kohen gadol's avodah on Yom Kippur, the Mishnah (Yoma 5:3) states, שֶׁעָמַד בַּמ ָּקוֹם וְעָמַד שׁ ֶנִּכְנַס לַמ ָּקוֹם נִכְנַס, "The kohen gadol entered the place he entered and stood at the place that he stood." From these words, we can take a lesson that on Yom Kippur, a person goes to the place and to the level that he prepared for himself before Yom Kippur.
The closing statement of the final Mishnah of Yoma is: ,הַטְּמֵא ִים אֶת מְטַהֵר מִּק ְוֶה מַה ,יְיָ יִשְׂרָאֵל מִק ְוֵה יִשְׂרָאֵל אֶת מְטַהֵר הוּא בָּ רוּ ךְ ׁהַק ָּדוֹש אַף , (Yirmiyahu 17) "Hashem is a mikvah for Yisrael. Just as a mikvah purifies the tamei, Hakadosh Baruch Hu purifies Yisrael." The Yalkut Gershuni quotes the Rambam (Hilchos Mikvaos, 1:9) which states, מְג ֻנֶּה זֶה הֲרֵי הַמִּק ְוֶה לְ תוֹךְ הַק ּוֹפֵץ, "He who jumps into the mikvah is disgraced."
Yom Kippur, we receive taharah like someone going to a mikvah, but we shouldn't jump in. We should prepare ourselves beforehand. The final Mishnah of Mikvaos states, לפני מטהרים אתם מי , "Before Whom are you purifying yourself?" Binah l'Ittim (drush 11) tells us that this means we should prepare ourselves before Yom Kippur arrives.