And Nadab and Abihu, the sons of Aaron, each took his censer and put fire in it, and put incense on it, and offered strange fire before Jehovah, which He had not commanded them. And there went out fire from Jehovah and devoured them, and they died before Jehovah. Then Moses said to Aaron, It is that which Jehovah spoke, saying, I will be sanctified in them that come near me, and before all the people I will be glorified. And Aaron held his peace. And Moses called Mishael and Elzaphan, the sons of Uzziel, the uncle of Aaron, and said to them, Come near, carry your brothers from before the sanctuary out of the camp. And they came near and carried them in their coats out of the camp, as Moses had said. And Moses said to Aaron and to Eleazar and Ithamar his sons, Do not uncover your heads nor tear your clothes, lest you die, and lest He be angry on all the people. But let your brothers, the whole of Israel, mourn the burning which Jehovah has kindled. And you shall not go out of the door of the tabernacle of the congregation, lest you die. For the anointing oil of Jehovah is on you. And they did according to the word of Moses. And Jehovah spoke to Aaron, saying, Do not drink wine nor strong drink, neither you nor your sons with you, when you go into the tabernacle of the congregation, lest you die, a statute forever throughout your generations. Even for a distinction between the holy and unholy, and between the unclean and clean and so that you may teach the sons of Israel all the statutes which Jehovah has spoken to them by the hand of Moses. (Leviticus 10:1-11)

1. It does not appear the they had any orders to burn incense at all at this time. It is true their consecration was completed the day before, and it was part of their work, as priests, to serve at the altar of incense; but, it should seem, the whole service of this solemn day of inauguration was to be performed by Aaron himself, for he slew the sacrifices (Lev_9:8, Lev_9:15, Lev_9:18), and his sons were only to attend him (Lev_10:9, Lev_10:12, Lev_10:18); therefore Moses and Aaron only went into the tabernacle, v. 23. But Nadab and Abihu were so proud of the honour they were newly advanced to, and so ambitious of doing the highest and most honourable part of their work immediately, that though the service of this day was extraordinary, and done by particular direction from Moses, yet without receiving orders, or so much as asking leave from him, they took their censers, and they would enter into the tabernacle, at the door of which they thought they had attended long enough, and would burn incense. And then their offering strange fire is the same with offering strange incense, which is expressly forbidden, Exo_30:9. Moses, we may suppose, had the custody of the incense which was prepared for this purpose (Exo_39:38), and they, doing this without his leave, had none of the incense which should have been offered, but common incense, so that the smoke of their incense came from a strange fire. God had indeed required the priests to burn incense, but, at this time, it was what he commanded them not; and so their crime was like that of Uzziah the king, 2Ch_26:16. The priests were to burn incense only when it was their lot (Luk_1:9), and, at this time, it was not theirs.
2. Presuming thus to burn incense of their own without order, no marvel that they made a further blunder, and instead of taking of the fire from the altar, which was newly kindled from before the Lord and which henceforward must be used in offering both sacrifice and incense (Rev_8:5), they took common fire, probably from that with which the flesh of the peace-offerings was boiled, and this they made use of in burning incense; not being holy fire, it is called strange fire; and, though not expressly forbidden, it was crime enough that God commanded it not. For (as bishop Hall well observes here) “It is a dangerous thing, in the service of God, to decline from his own institutions; we have to do with a God who is wise to prescribe his own worship, just to require what he has prescribed, and powerful to revenge what he has not prescribed.”
3. Incense was always to be burned by only one priest at a time, but here they would both go in together to do it.
4. They did it rashly, and with precipitation. They snatched their censers, so some read it, in a light careless way, without due reverence and seriousness: when all the people fell upon their faces, before the glory of the Lord, they thought the dignity of their office was such as to exempt them from such abasements. The familiarity they were admitted to bred a contempt of the divine Majesty; and now that they were priests they thought they might do what they pleased.
5. There is reason to suspect that they were drunk when they did it, because of the law which was given upon this occasion, Lev_10:8. They had been feasting upon the peace-offerings, and the drink-offerings that attended them, and so their heads were light, or, at least, their hearts were merry with wine; they drank and forgot the law (Pro_31:5) and were guilty of this fatal miscarriage.
6. No doubt it was done presumptuously; for, if it had been done through ignorance, they would have been allowed the benefit of the law lately made, even for the priests, that they should bring a sin-offering, Lev_4:2, Lev_4:3. But the soul that doth aught presumptuously, and in contempt of God's majesty, authority, and justice, that soul shall be cut of, Num_15:30.