Leviticus 10:3

And Mosheh said, This is that which the Lord spake with me in Sinai, saying: In them who come near before Me I will have the tabernacle to be sacred, that, if they be not heedful in the service of the oblations, I will burn them with flaming fire from before Me, that in the sight of all the people I may be glorified. And Aharon heard, and was silent; and he received a good reward for his silence.

This is what God has told me God has already told me that He will manifest His holiness through those who are near Him — even if they must suffer for it, as in the passage “You only have I known…” [Amos 3:2]. Thus the verse means, “When I manifest myself in holiness among them, then I shall be glorified; and I shall be glorified in the face of all the people, and they shall fear Me.”

THIS IS THAT THE ETERNAL SPOKE, SAYING: ‘THROUGH THEM THAT ARE NIGH UNTO ME I WILL BE SANCTIFIED.’ “Where had He spoken this? In the verse, and [the Tent] shall be sanctified ‘bichvodi’ (by My Glory). Do not read the word as bichvodi (by My Glory) but bimechubodai (through My honored ones). Moses said to Aaron: ‘My brother Aaron, I knew that this Sanctuary was to be hallowed by those who are beloved of the Holy One, blessed be He, and I thought that it would be either through me or through you. Now I see that your sons were holier than I and you.’” Thus the language of Rashi, based on the interpretation of our Rabbis. But if so, the verse, and [the Tent] shall be sanctified ‘bichvodi’ means “that it will become holy in the eyes of all the people through my honored ones, and they will know that I dwell therein.”
Rabbi Abraham ibn Ezra also wrote: “This is that the Eternal spoke, saying, means: G-d had already told me that He would show His sanctity through those that were near to Him. This is similar in meaning to the verse, You only have I known of all the families of the earth; therefore I will visit upon you all your iniquities. And when I will show them this holiness of Mine, then I will become glorified before all the people and they will fear Me.” But if this is so, then this is a statement not written [in the text], that G-d informed Moses of His ways and that such is the nature of His attribute!
In my opinion there is no need for all this. For by way of the plain meaning of Scripture, the expression “G-d spoke” refers to His decrees, His thought, and the manner of His ways, and the term “speaking” is used with reference to all these [in humans]. Thus: I spoke with my own heart, means “I reflected on this thought.” And this is ‘hadavar’ that Joshua did circumcise, means “this is ‘the cause’ why Joshua did so.” ‘Al d’var’ (because of) the money. Similarly, And let her be thy master’s son’s wife, as the Eternal hath spoken,, 24:51. means “as He hath decreed.” Likewise: In his days did Hiel the Beth-elite built Jericho; with his firstborn he laid the foundation thereof, and with his youngest son Segub he set up the gates thereof; according to the word of the Eternal, which He spoke by the hand of Joshua the son of Nun. Thus Moses said here: “This incident is that which G-d decreed, ‘saying to His heart': Through them that are nigh unto Me I will be sanctified so that they should not break forth into My sanctity; and before all the people I will be glorified, so that they treat My dwelling-place with respect.”

this is when Moses said to Aaron: “do not mourn nor weep, and do not desist from carrying on with your priestly duties; I am telling you what I am saying in the name of G’d Who has said: בקרובי אקדש, I want to be sanctified by the High Priests, the ones who are “near” to Me and who perform the service for Me. I do not want that they should desecrate My name and My holy service by letting their private concerns take precedence.” Moses added that G’d had specifically given him instructions concerning such events as had just happened by saying (Leviticus 21,10-12) “the priest who is exalted above his fellows, on whose head the anointment has been poured and who has been ordained to wear the vestments, shall not bare his head nor rend his vestments. He shall not go in where there is a dead body; he shall not defile himself even for his father or mother. He shall not go outside the sanctuary and profane the sanctuary of his G’d, for upon him is the distinction of the anointing oil of his G’d, Mine the Lord’s.” It follows that by not leaving the holy precincts at this time Aaron did in fact sanctify the name of the Lord. This is the meaning of בקרובי אקדש, “I will be sanctified by those close to Me.” The fact that the legislation we just quoted appears only in chapter 21 is no argument as the Torah is not bound to record its message to the Jewish people in chronological sequence. At any rate, Moses told Aaron not to abandon the service in the Tabernacle while in circumstances which imposed mourning on other priests, even.

ועל פני כל העם אכבד, this is the “honour” accorded to G’d’s Presence that even when one sees one’s sons dying one ignores one’s personal grief and continues with the service to one’s Creator.

וידום אהרן, he desisted from his mourning, did not weep and did not perform rites of the mourning.

וידום אהרן, seeing he consoled himself after having been told that the death of his sons represented a sanctification of the name of the Lord.

בקרובי אקדש, “I will become sanctified by means of the people who had been close to Me.” The very death of these people is an event which sanctifies Me. How so? If the Israelites will internalise how strict I have been with these highly placed individuals, they will know how careful they have to be not to deviate from My commandments.