Parashat Acharei-Mot begins with the procedure of the Kohen Gadol's entry into the Kodesh Kodashim. It is introduced with a warning to the Kohen Gadol lest he treat the occasion with less than the required awe and dignity. Then the Torah sets forth the way in which the Kohen Gadol is to enter: the sacrifices that he must bring for himself, the goats which he must take from Bnei Yisrael, the special garments that he is to wear, and a detailed order of service, including bringing a censer of burning coals with incense into the Kodesh Kodashim.

What is the connection between the order of service as set forth here and the "death of the two sons of Aharon, when they drew near to God, and they died"? 

Through an examination of the text, we can understand that the tikkun for the sin of Nadav and Avihu is the integration of the private religious experience of the Kohen Gadol with a sense of connection to the people and his identity and role as their emissary. The Kohen Gadol's right to enter the Kodesh Kodashim and to experience the uplifting and sanctity of this proximity to the Divine Presence arises not from his personal status, but rather from his role as the representative of Am Yisrael. 

Courtesy of the Virtual Beit Midrash, Yeshivat Har Etzion