Only What Is Commanded
The death of the two sons of Aharon has many explanations. The Chidushei Harim gives his own novel interpretation of this incident.
He pointed out that Nadav and Avihu were extremely holy men on a very high level. Their intentions were for the sake of Heaven.
In their zeal to achieve this holiness, they failed to recognize one important matter. The Pasuk says that they offered an אש זרה, “a strange fire,” followed by the key words, אשר לא צוה אותם, “that they were not commanded.”
No matter how “frume” a person might think he is, he must be careful to act solely in the manner that comes from Hashem’s command.
It is essential even for the well intentioned, not to allow things to get out of control. There is a reason why our Torah has such clearly defined laws. One must not leave the boundaries of Halacha. This can happen when one is lax in his observance, and it can also apply when one is overly zealous.
Nadav and Avihu left the boundaries of the Torah when they did something that “they were not commanded.” Because of the high level they were on, they paid with their lives. A clear statement needed to be made for future generations as to how to observe the Torah. One must not go “out of bounds.”