Please read Leviticus 10:1-7 before continuing!
Stories like this are always extremely confusing to me because it seems so crazy that God would destroy someone for making what seems to be a little mistake. These stories are also very powerful weapons used by those who fight against the reality of God and Christ because many Christians don't know how to respond or haven't even heard the stories. (Being able to stand up for God is another incentive to know and treasure His word.) Although I may never understand the reason behind this particular action in it's entirety, the explanation given in my study notes made a lot of sense. It is paraphrased below.
Even though they had just listened to the explanation of God's personal instructions (Leviticus 1-7), watched them preformed (Leviticus 8-9:21), and visually seen the presence of God (Leviticus 9:22-24), they used the wrong kind of fire when the sacrificed their offering to the Lord. The fire on the Alter used for sacrifice was holy because God's greatness and goodness and holiness demanded that everything the Israelites worshiped Him with was holy (This changed after Jesus came. Now, through His grace, we can worship God however we feel lead by the Holy Spirit which is the way God originally intended anyway! Thanks JC!) Nadab and Abihu were being careless in their service and worship of God. The instructions for how to relate to God are part of His law so preforming the sacrifices was an act of obedience and doing them correctly showed respect. Nadab and Abihu had been placed in a position of leadership so they had a special responsibility to obey God because the people would follow their lead. However, instead of taking care to obey God and not lead His people astray, one of their first acts as priests (they were still in the ordination process and this could be their first since no others are mentioned) showed disrespect and disobedience to God's law. You know the story Jesus told about the master and the talents (Matthew 25:14-30), Nadab and Abihu are like the first man. As priests, the were respected, taken care of, and got to spend their time serving God in the beautiful tabernacle tent. But, they were careless with what they'd been given and received their due reward.**
So, what can we learn from the story of Nadab and Abihu? We can learn what it means to be a leader for Jesus. When God puts us in a position to lead, it is extremely serious because God's people are what He loves most in the world and when we lead, He has trusted us with what is most precious to Him. If God has commissioned you to lead or teach others, never take that role for granted or abuse it. Stay faithful to God and follow His instructions.
*Does this mean they aren't in heaven? Who are any of us humans to say? Nadab and Abihu and real people and their story is a true story, God has told us what we can learn from and no more.
*Many people argue against Christianity by claiming the the fiery God of the OT is very different from sweet, loving Jesus in the NT. As a follower of Jesus, it is important that we know the truth, Jesus is God. (John 10:30; 1 Tim. 3:16; John 8:19; John 1:14) But just as important as it is to know and believe the verses that spell it out for us, it is also important to recognize that fact. The story of Nadab and Abihu can be easily related parable of the talents. Just as Nadab and Abihu were severely punished for their disrespect and disobedience toward God, so was the third servant and all three were severely punished. There are many other similarities between Jesus' teaching, God's instruction, and the event of the OT. But to me, the most significant is the fact that from the moment Adam and Eve sinned, God (in His three parts) had a plan to sacrifice Himself to save us. He alluded to Jesus all through the OT which shows that He never changed His mind or love in regards to us and the salvation plan.
Food for Thought: According to John 1:14, God (the threesome) is the perfect balance of grace and truth. When God kills Nadab and Abihu, He's displaying the truth side of Himself. He flat out said bad things would happen to those who disobeyed the laws created by God for their own good. But what if He was also showing grace to His people by eliminating the opportunity for them to have been led astray by two of their first priests. Obviously this could be completely wrong but I thought it was interesting to think about.
Reassurance: One way that we are assured that they weren't consumed by the fiery wrath of God for a little accident is what next happens with their two brothers, Eleazar and Ithamar. Read Leviticus 10:16-20. The two brothers were confused, sad, and probably quite scared. They did what they thought would be best based on God's law and their own feelings. While it probably would have been best for them to go ahead and follow God's law despite their emotions, God won't punish us for doing things wrong on accident in our confusion or grief. What matters to Him is that we are doing our best to obey Him and ask forgiveness when we don't get it right.
Expansion on the Chronological Life Application Study Bible
p.s. the last 2 sentences from the "So, what can..." paragraph are verbatim from my Bible.