Purpose of the Service of Vayikra 16/2

The Service of Acharei Mot

Exegetical Approaches

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Atonement for the People

The central focus of the service was to achieve Atonement for all of Israel, and any part of the service that has to do with purification of the Mikdash is just a means to the ends of Atonement

Sources:R. Saadia GaonCommentary Vayikra 16About R. Saadia Gaon,

Why start with Nadav and Avihu? To achieve atonement for the people, it is required for Aharon to go into the Holy of Hollies. Since according to R. Saadia Gaon (verify this) explains that Nadav and Avihu were killed for going into the Holy of Hollies, Hashem used them as an example for what could happen if you go into the Holy of Hollies without the accompanying service.

What sins are being atoned for? The atonement from the service is for all of the sins of Israel.

Is the purification for the people or the place? The purification is for the people exclusively. Any reference to purifying the Kodesh or any part of the Mikdash is not to be understood as purifying the place or objects themselves; instead these objects are facilitating the atonement through the service of the day.

Purification of the Temple

The main focus of the service is to purify the Mikdash from impurity. All issues that deal with atonement are just a byproduct of rectifying the impurity in the Mikdash.

Sources:Hoil MosheVayikra 16:1Vayikra 16:2Vayikra 16:3Vayikra 16:11Vayikra 16:16Vayikra 16:23Vayikra 16:32Vayikra 16:34About R. Shelomo Yitzchaki, ShadalVayikra 16:1Vayikra 16:8Vayikra 16:16Vayikra 16:30About R. Shemuel David Luzzatto, Milgram , 

Why start with Nadav and Avihu? Since the death of Nadav and Avihu caused the Midash and certain utensils to be impure, there is a need to purify them through this service.

What sins are being atoned for? It depends on whether the impurity is a Halakhic or Metaphoric: 

• Metaphoric - There must be atonement for all the sins of Israel that are causing the Mikdash to be impure.
• Halakhic - There is only atonement for sins directly dealing with the impurity of the Mikdash, i.e., Making the Mikdash impure, eating sacrifices in an impure state, etc. 

Is the purification for the people or the place? The purification is for the Mikdash that has become impure. Any reference to the atonement of Israel's sins is a means to purify the temple.

Is there a greater atonement? The biggest issue with claiming the service on Yom Kippur is solely about purification of the temple is a later verse of the chapter (16:30):

כִּי בַיּוֹם הַזֶּה יְכַפֵּר עֲלֵיכֶם לְטַהֵר אֶתְכֶם מִכֹּל חַטֹּאתֵיכֶם לִפְנֵי י"י תִּטְהָרוּ.

For on this day shall atonement be made for you, to cleanse you; from all your sins shall ye be clean before the Lord.

 The verse seems to say that there is a universal atonement that happens on this day which is connected to the service of the day. One way of solving this issue is to say that there is a separate aspect of atonement on Yom Kippur that has nothing to do with the service done by the Kohen Gadol.¹ 

A Greater Purpose

Both purifications of the Mikdash and Atonement for the people are only a part of a greater whole which is the real reason for the Yom Kippur service.

Allow the Divine Presence to stay in the Temple

Sources:NetzivVayikra 16:16About R. Naftali Tzvi Yehuda Berlin

What causes the Divine Presence to leave the Temple? According to the Netziv, two things cause the Shekhina to leave the Mikdash:

• Desecrating the Mikdash with a Halakhic impurity
• The sins of Israel 

To keep the Shekhina in the Mikdash and with Israel, the Yom Kippur service is needed to purify the physical place of the Mikdash and to achieve atonement for the sins of Israel. With both of these tasks accomplished the Divine Presence could stay in the Mikdash amongst Israel.

Why Nadav and Avihu? The procedure of purifying the Temple and achieving atonement for Israel requires an incense offering in the Holy of Hollies. Since according to the Netziv Nadav and Avihu were killed because they brought a strange fire into the Holy of Hollies, Hashem, therefore, warns Aharon before he goes into the Holy of Hollies what can happen if one goes in with the wrong procedure.² 

What sins are being atoned for? All the sins of Yisrael need to be forgiven

¹ Support for this understanding can be seen in the verses as the mention of the service has to be done on Yom Kippur comes after the service itself. The Meshekh Chokhmah points this out and posets from the Gra that the service was able to be done on other days besides Yom Kippur to purify the temple.1
Another proof to this is the Mishna Yoma where R. Akiva lauds Israel for being purified by Hashem. Rav Soloveitchik2 understood this as R. Akiva telling the people, in a post-second temple world Israel still gets atonement from Hashem without the service of Yom Kippur. Seemingly, in this understanding, the day of Yom Kippur itself atones for the sins of Israel and the above verse is a declaration of that and not connected to the purification of the Mikdash.

² Additionally, the deaths of Nadav and Avihu may have defiled the Mikdash, and therefore it needed a purification. Recalling their deaths may have been a call to Moshe and Aharon to purify the Mikdash so the Shekhina could continue to reside there.