Fivefold ministry refers to Ephesians 4:11-16 where the five primary gifts of the New Testament Church are enumerated:
1) Apostles
2) Prophets
3) Evangelists
4) Pastors
5) Teachers
Not only does this passage tell you what the offices of the fivefold ministry are, but it tells you the three-fold purpose of God setting these gifts in the Church.
1) Perfecting of the saints
2) The work of the ministry
3) Edifying of the Body of Christ
Without a fivefold ministry, you do not have the fullness of Jesus Christ represented in that assembly. Why? Because Jesus represents the fullness of ministry. Jesus is the Apostle of our profession (Hebrews 3:1), Jesus is the Prophet that should come (John 4), Jesus is the great Evangelist who came to seek and save the lost and to preach good tidings of good things (Luke 19:10, Isaiah 61:1-3), Jesus is our Pastor/good shepherd who watches over us (John 10:11), and Jesus is our Teacher come from God as Nicodemus testified (John 3:1-5). Jesus received the Spirit without measure (John 3:34) and when he walked this earth, he chose twelve men to teach, train, and ordain to continue the work of the Kingdom of God after His ascencion. Since then, God has been apprehending men for fivefold ministry work by teaching them, training them, and ordaining them to be His representatives here on earth to help God's people reach perfection. The fivefold ministry operates directly under Christ, who is the head of the Church. The fivefold ministry is not the head of the Church. Once again, Christ is the head of the Church. The fivefold ministry simply recieves instructions from Christ and blesses God's people with the gifts they have been given for that purpose.
You are only as strong as the ministry you are under. This seems like a strong statement, but it is a very real statement. As saints we trust that God has led us to a Church where the ministry is strong in the Lord, faithful, God-ordained, able to teach, preaches and teaches sound doctrine, etc. But, we can only learn as much as has been revealed to them, right? We can learn in many ways... directly from God, from God's people speaking under the inspirition and backing of the Spirit of God, the spoken/written word of God, etc. There are so many ways to learn, but time and time again you see that God sends His messengers to deliver his commandments and judgments to the people. So, the fivefold ministry plays a big role in our spiritual progress. And if a Church does not believe in the fivefold ministry then that Church is missing the mark. Fivefold ministry is necessary for saints to reach perfectoin (this is, once again, directly from Ephesians 4:11-16). To the naysayers, my question is this: What stops God from raising up Apostles in these days? What stops God from raising up Prophets in these days? What stops God from raising up Evangelists in these days? What stops God from rasing up Pastors in these days? What stops God from raising up Teachers in these days? Jesus himself called and chose twelve Apostles, what stops him from doing the same thing in these days? I believe it is vital for every Church to understand God's order is fivefold and all five offices work together in unity to preach the gospel and save souls for the Kingdom of God. If you have time to do further study, it is amazing how all five gifts specialize in certain things, but all are for one and all for all.
Fivefold ministry is a wonderful thing. God intends it to be this way. Look how beautiful it was in the early Church and how they turned the world upside down for Christ. So, I say let's stop saying this gift is for today and this gift is not for today. Let's buckle down, let's pray for God to raise up able ministers of the New Testament and let's all work together for the glory of God.
Samrod, I hope this summarizes what the fivefold ministry is and why it is important for New Testament Churches today. There are, of course, so many things to talk about this subject, but this I hope was a good summary.