The question centers on just what is profane fire (or strange fire in some translations). To be perfectly honest, no one really knows. It seems like they are following the prescribed order of things according to the instructions of Lev. 16:12 (instructions they would have known, but were not yet recorded by Moses).
We can only guess that maybe they used improper incense, forbidden in Ex. 30:9, or that the fire (coals) they retrieved for their censers were not from the altar, but from some other source. Several books guess about their motives stating 1) they were in a hurry, 2) they were anxious about their first day on the job and so were unsure about a few things 3) they did so intentionally 4) they were lazy. But whatever their intention or motivation was we are not told.
What we do know for certain is that as priests they were set aside to be holy unto God and in service they failed in their first attempt to offer incense to God.
I believe we are not informed about their inner intentions and motivations for a reason. If we knew their attitude was one of knowing a better way of making incense, we would charge them as God did, for thinking they knew more than the omniscient God of all creation. If they only grabbed from the wrong spice jar, we might begin to question their death sentence. The idea of not knowing is so that we, the readers, are not left in the middle position of getting to pass judgment upon God or the men. God has passed judgment without our consent and will not be held to our faulty and sinful “that’s not fair” attempts at mediation. This is something we almost instinctively hold against God whenever we read about poor Uzzah in 2 Samuel 6:6-7. All he was trying to do was steady the Ark, but both cases are open and shut cases of disobedience.
It all seems pretty harsh huh? See, it all just depends on just how offensive we really believe our sins to be. Are all of our sins (big or teeny-tiny known only to us) really all personal offences against God or just mistakes in judgment? This is where we get into meaning and application phase of the passage. The application is as far reaching into our day, being we see a similar pattern. Found in Acts 5:1-11, we have the story of Ananias, with Sapphira his wife, who sold property and held back a portion, yet stating they are giving the apostles “all” the proceeds.
Typically these passages (together or separately) say a lot about how Christians are to perceive worship and the holy character of God. Churches have even divided about where or not there is such a thing as a “regulative principle” for worship, prescribed throughout the Bible that needs to be followed or is it just do whatever feels good (I state that as an extreme). What I believe we should do when we encounter passages such as these, is to stop, and consider (as a whole church body at times, not just as individuals) if we are offering God proper worship. The exhortation of 1 Corinthians 11:27-30 seems really relevant that in the early church some were dying for an improper respect for the Lord’s Supper, not acknowledging the holy presence of God.
Aside from this being the typical (and a correct exhortation), I’d like to add another observation that this has even more to do with God’s holiness. Not just in forms of worship (where we are usually the passive one sitting in a pew ready to judge others), but in our own lives we should be seeking and striving for holiness. God may save us just as we are (thinking of that “just as I am” hymn), but He does not leave us that way, there is a change. As amazing as the times of Lev. 10 and Acts 5 were, and all the things they would have witnessed, still these four people were clinging too much to their sin. All four were carried out of the presence of God dead.
Are there any profane fires being offered today in churches? Sure there are. Are we stricken dead all the time? By the grace and mercy of God, No we are not. Yet God by His mercy and grace should be no less respected. It used to be a reverent pun that a nonbeliever would not want to set foot inside a church for fear of lightening striking them (they had heard of these passages to some extent). The church took seriously that church was holy ground, because God was about to meet with His people there. There were things that you just didn’t do in the presence of God when joined for worship. Today it’s anything goes. There is no offence or fear of anything but more of an appeal to come on in the water’s fine.
I fear for churches who have tossed preaching aside (I refer to real exegetical preaching, not what passes for “preaching” in most places) for other entertainments. I can’t imagine standing before almighty God and trying to defend myself saying, “Lord, Lord, have we not had puppet ministries in Your name, cast out Mormons in Your name, and done many concerts in Your name?” (Matthew 7:22 paraphrase mine). Not trying to state these things, in and of themselves are all evil or anything, but to me they do not pass for prescribed worship. All these things occur when man sits himself in the place of God and states, I know a better way to do this.