After the death of the two sons of Aaron (Leviticus 16:1)
Rabbi Elazar ben Azariah would explain this with a parable. A sick person was visited by a physician, who said to him: “Do not eat cold food and do not lie in the damp, lest you die.” There then came a second physician, who said to him: “Do not eat cold food and do not lie in the damp, lest you die as so-and-so died.” The second one influences him more than the first. Thus it says: “After the death of the two sons of Aaron.”
(Rashi)
Who came close to G‑d and died (16:1)
They approached the supernal light out of their great love of the Holy, and thereby died. Thus they died by a “Divine kiss” such as experienced by the perfectly righteous; it is only that the righteous die when the Divine kiss approaches them, while they died by their approaching it. . . . Although they sensed their own demise, this did not prevent them from drawing near to G‑d in attachment, delight, delectability, fellowship, love, kissing and sweetness, to the point that their souls ceased from them.
(Ohr HaChaim)
He shall bathe his flesh in water, and clothe himself in them (16:4)
On that day the kohen gadol immersed (in a mikvah) five times, and washed his hands and feet from the kiyor (basin) that stood before the Sanctuary ten times: each time he changed his clothes he was required to immerse once and wash twice (once before removing the first set of clothes, and again after dressing in the second set).
For there were five sets of services performed by him on that day: 1) The regular morning services, performed in the “golden garments” (worn by the kohen gadol throughout the year). 2) The special services of the day (reciting the confession over the Yom Kippur offerings, casting the lots, entering the Holy of Holies to offer the ketoret and to sprinkle the blood of the Yom Kippur offerings)—performed in the linen garments. 3) The two rams brought as “ascending offerings,” and the day’s musaf offerings—in the golden garments. 4) Returning to the Holy of Holies to remove the pan of burning incense—in the linen garments. 5) The regular afternoon services—in the golden garments.
(Talmud, tractate Yoma)
They should be identical in appearance, height and price, and should be acquired together.
(Talmud, Yoma 62b)
And so shall he do for the Tent of Meeting, which dwells amongst them in the midst of their defilement (16:16)
Also when they are in a state of defilement, the Shechinah (Divine Presence) dwells with them.
(Talmud; Rashi)
For on this day, He shall atone for you (16:30)
On Yom Kippur, the day itself atones . . . as it is written, “For on this day . . . shall atone for you.”
(Maimonides)