Our Gemara on Amud Beis describes a vision that Shimon Hatzaddik had on his last Yom Kippur, which led him to conclude that he would not live to serve next year:

“Shimon HaTzaddik said to them: In previous years, every Yom Kippur, upon entering the Holy of Holies, I had a prophetic vision in which I would be met by an old man who was dressed in white, and his head was wrapped in white, and he would enter the Holy of Holies with me, and he would leave with me.

But this year, I was met by an old man who was dressed in black, and his head was wrapped in black, and he entered the Holy of Holies with me, but he did not leave with me. Shimon HaTzaddik understood this to be a sign that his death was impending.”

Who was this “Man” that accompanied him each year? 

Tiferes Shlomo (Yamim Tovim, Yom Kippur 5) gives us more background as he works through textual anomalies in the verses (Vayikra 16) that describe the Yom Kippur service. The entire piece constantly refers to what “Aharon the Kohen” should do. The reality is, that it was an order dictated to be performed by every Kohen Godol on Yom Kippur. The verse states, chukas olam - an everlasting law (ibid 16:34), so why insert Aharon here? Another question, more in the style of derash, is the Talmudic dictum: “all parts of the Yom Kippur service are valid only when performed by him.” (Yoma 73a). Technically, this is not true, as the slaughtering can be performed by a non-Kohen. An additional derush-style question is that the verse (Vayikra 16:17) states: “and no man shall be in the Tent of Meeting..” How can no man be there, he, tge Kohen, a man, is there?

Tiferes Shlomo says the meaning is that no one can enter as a man. The Kohen must shed his physical presence and become a spiritual entity. The verse should read, “and no one manifesting as man shall enter.” How did the Kohen Godol of each generation achieve this? Through the presence of Aharon’s spirit who came to meet them. This is why the verse states “Aharon Hakohen” because on every Yom Kippur the spirit of Aharon performs the service. This is the hidden intent in the Talmudic dictum “all parts of the Yom Kippur service are valid only when performed by him.” Meaning, the service is only effected by channeling the original Aharon Hakohen to accompany in the service.

We should reflect on why the Yom Kippur service involves a manifestation of Aharon. This is unlike any other service. And if we should have any manifestation it should be Moshe, who achieved forgiveness for the Golden Calf. It is hard to say precisely, but Aharon and Yom Kippur are intertwined via the sin of the Golden Calf. Aharon had a role in the Golden Calf (Devarim 9:20 and Rashi Vayikra 9:2) and Yom Kippur originated from the process of forgiveness for the Golden Calf, see Rashi Devarim 9:18.

We can think of Yom Kippur as a day that Aharon’s power of achieving forgiveness is most manifest.

A final and related thought. The high priest must ironically occupy this lofted role but also humbly bear the sins of himself, his family and the Jewish people (Vayikra 16:17). He had to be great and humble. Being reminded that the great Aharon also can sin and needs forgiveness is the spirit he must draw from to enter into the Holy of Holies. The Kohen who can enter and emerge safely is one who is honest with himself and God about his sins.