Acts 1:23-24
So they proposed two men: Joseph called Barsabbas (also known as Justus) and Matthias. Then they prayed, "Lord, you know everyone's heart. Show us which of these two you have chosen...
The community of believers gather together to pray after the resurrection and ascension of Jesus. It is an very Jewish community. There are 120 of them - this is the required number of people needed to form a synagogue with its own council. It also consists of twelve apostles who were sent on mission to Israel, and who would sit on twelve thrones to judge the twelve tribes of Israel...except it doesn’t.
Judas, after he betrayed Jesus became so overcome with guilt that he killed himself, and so it is necessary for the apostles to appoint someone to replace him. The book of the Acts of the Apostles begins with a betrayal by one of the Apostles. We are reminded that community of believers is fallible, that attack can come from those who have followed Christ.
The person to replace Judas must, according to Luke, fill the same criteria that the other apostles met. This is to say that they must be eyewitnesses to the events from Jesus’ baptism until he was taken up into heaven. Although these criteria would not include the Apostle Paul (presumably he wouldn’t agree with them then), they show luke’s concern for making sure that there is a faithful witness to the life and ministry of Jesus.
The new leader then must be qualified, but must also be chosen by God. This fledgling community needed a leader, and so the church today needs leadership - of course the nature of this leadership is much debated. In the next chapter the Holy Spirit is poured out on everybody meaning we are all chosen and all have qualifications to be leaders, but God still calls some to be servants (and leaders) of the leaders.