I was asked about the relationship between Nadab and Abihu’s death and the Day of Atonement ceremony. I responded as follows:
Remember that these two saw the Lord in sacred space (on top of Sinai with Moses) earlier in their lives. (Exo. 24: 9-11)
Despite their earlier audience with the Lord, they were not authorized to enter the Holy of Holies. Only the chosen High Priest, and then once an year, only on the Day of Atonement. (Lev. Chapter 16; 23: 26-32.)
They entered into the Holy of Holies when they were not authorized, and burned incense contrary to the Day of Atonement ceremony. They were not authorized to be there nor to do what they did. Therefore they were struck down. (Lev. 10: 1-3.) The Lord reminded Moses after their death that those who are going to enter into that place must be “sanctified” before entering, hence the Day of Atonement ceremony being a prerequisite for entry.
Later Jewish tradition required the High Priest to have a rope tied to his ankle when he entered the Holy of Holies, so that his body could be recovered if he were struck down without the necessity of others entering the room.