What does Acts 6:3 mean?
Although the passage doesn't use the word, this is the establishment of the office of "deacon" in the church. Diakonia, the Greek root word from which "ministry" comes, specifically refers to the role of the deacons who collect and disperse resources (Acts 6:1–6); it is also used in the more general sense (Acts 20:24). It means to serve others by command of someone else. A small leadership staff cannot fill every need in a church. Forcing infinite responsibility on them is disrespectful to non-staff who have gifts of their own.Throughout the history of Christianity, God has used conflict to refine belief and understanding. Until this time, the Holy Spirit worked in the hearts of the Jesus-followers to take care of each other's practical needs (Acts 2:44–45; 4:32–37). There is nothing wrong with this system of management if the group is small and the members diligent and attentive. There are now thousands of Jesus-followers in Jerusalem, and the benevolent mob can't keep track of everyone.
The church leadership needs some structure. Not only are the apostles willing to hand over responsibility for managing money and assets, they're willing to let others choose the candidates who will do so. This delegation of duties is consistent with the Old Testament. Moses wisely agreed to place the Israelites under the command of a hierarchy of leaders (Exodus 18:19–23). And Nehemiah established quartermasters to make sure the Levites received their due (Nehemiah 13:13).
The leadership structure of the church is different than that in the Old Testament, however. God set aside the people of the tribe of Levi to serve Him. He designated that priests would come from the line of Aaron. The other Levite families had specific duties regarding the tabernacle (Numbers 3:21–37). Their tasks were based on what family they belonged to. In the church, however, leadership isn't based on family but character. First Timothy 3:8–13 lays out the qualifications for deacons, most of which deal with integrity. While deacons need to be spiritually mature, as any church leader, the apostles especially need to know they will handle the finances honestly and responsibly.