There are a few things going on here, but in a word, God is reorganizing. Let’s tackle the events in order. First, the Lord has ordained that for the purpose of ministering to the needs of His Tabernacle, the first-borns of every tribe of Israel will be replaced by the first-borns of the tribe of Levi. Collectively we all may ask, “Why?”
…Then Moses stood in the entrance of the camp, and said, “Whoever is on the Lord’s side–come to me.” And all the sons of Levi gathered themselves together to him. Exodus 32:26
There’s your reason. Remember the golden-calf incident in Exodus 32? Well the Levites were the only ones who stepped when Moses made the call. Their reward comes a year later (at this time) when God made their ordination official—the tribe of Levi is the ministering clan of His dwelling place.
And why are the first-born the Lord’s? Unquestionably all creation is the Lord’s, but God’s right (for lack of a better word) to claim the first-born of Israel came about during the first Passover when He spared them all from certain death, therefore no one else can make claim to this cluster of people.
Redemption
As we read the Numbers text we first notice that the numbers do not add up. That is to say there are 22, 000 Levites and there are 22, 273 first-born slots to be filled, leaving a balance of 543 shoes to fill (did you get the math?). God in His infinite wisdom concluded that the only remedy was redemption—a price would have to be paid. Why does God resort to this solution? Only He knows in entirety, but it certainly does lay the ground work for a deliverance procedure all Christians have become familiar with.
Or do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own? For you were bought at a price; therefore glorify God in your body and in your spirit, which are God’s. 1 Corinthians 6:19-20
Is This the Backbone of Replacement Theology?
No. Replacement theology–the notion that the body of Christ, His church has somehow replaced the nation of Israel, is a false doctrine and it is certainly not what is being illustrated here. Replacement does not mean displacement. What it does mean is that the replaced have lost out on the double-portion customarily awarded to the firstborn. There is a cost for disobedience and we do reap what we sow, but as long as there is repentance towards Christ Jesus there remains an open door to salvation. The church of Jesus has been grafted into the vine; we have not swapped-out the old for the new.
But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light; who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy. 1 Peter 2:9-10
He Dwells -- The B'log in My Eye 