Why does the Torah not tell us right at the outset that this order of service is meant to be carried out on Yom Kippur? It would seem that the Torah wishes to teach us not to rely on the holiness of Yom Kippur, but to make the effort to fulfill all the details involved in the service we are commanded to carry out.
Chapter 16 deals entirely with all the minute details of the order of service on Yom Kippur. One would therefore have expected to find the crucial fact that the order was to be carried out on Yom Kippur at the start of the chapter. Yet, surprisingly, Yom Kippur is not mentioned until the verses following details of the order of service (16:30). What is the meaning of this inversion and what can we learn from it?
With all the minute details that are listed, it would seem that the Torah wishes to stress to us that we may not belittle these details and rely on the inherent holiness of the day itself and on our good intentions in order to achieve atonement without paying attention to all the details God commands us to do. On the contrary, we are required to make the effort to carry out God's will with the understanding that it is His will that knows how to provide the fine details and build a perfect edifice based on them. His will is the ultimate decider.
Aharon's two sons thought otherwise. They felt they could determine the best way to express their dedication to God. Their sin was that they brought fire and incense that they had not been commanded to without waiting for the fire to descend from heaven and without understanding that in this mistaken order they are fulfilling their own desires and not the will of God.
Therefore, as the appropriate atonement for Nadav and Avihus' sin, the Torah states at the opening of the order of the service that these instructions were given to Moshe "after the death of Aharon's two sons, when they drew near before the Lord, and they died". In this way, the Torah stresses to us not to follow in the way of Aharon's sons who wished to get come close to God at an inappropriate time and in a manner in which they had not been commanded.