Acts 1:15-20 meaning

While waiting for the Spirit to come as Jesus promised, At this time Peter stood up in the midst of the brethren (a gathering of about one hundred and twenty persons was there together), and spoke.

The brethren included the female disciples as well. The previous passage only listed the eleven apostles, the women, and Jesus's mother and brothers. That there were one hundred and twenty persons in that upper room together shows the remnant who followed Christ, and were waiting together in obedience to His command.

So Peter spoke, some matter weighing on his mind: Brethren, the Scripture had to be fulfilled, which the Holy Spirit foretold by the mouth of David concerning Judas, who became a guide to those who arrested Jesus. For he was counted among us and received his share in this ministry.

Judas Iscariot had served for three years alongside these other men. But ultimately he betrayed Jesus, and became a guide to those who arrested Him, leading the soldiers of the Pharisees to where Jesus prayed on the Mount of Olives (Luke 22:47). Judas was formerly counted among the apostles, and had received his share in the ministry given to them by Christ. Peter discerns that by the mouth of King David, through his poetry, the Holy Spirit foretold the fate concerning Judas. This means that the Holy Spirit had inspired David in his writings, that they referenced the future event of Judas's removal from apostleship.

We are reminded by Luke of what became of Judas after he betrayed Jesus: Now this man acquired a field with the price of his wickedness, the thirty pieces of silver paid to him for revealing Christ's location. And so, falling headlong (after hanging himself, Matthew 27:5), Judas burst open in the middle and all his intestines gushed out. And it became known to all who were living in Jerusalem, the news of this suicide spread throughout the city; so that in their own language that field where Judas killed himself was called Hakeldama, that is, Field of Blood.

After reminding his readers that Judas was no longer among the twelve, Luke continues to recount Peter's statement. Peter is referencing David's writings, relating them to the matter at hand:

"For it is written in the book of Psalms,
'Let his homestead be made desolate,
And let no one dwell in it';
and, 'Let another man take his office.'

Peter references two Psalms written by King David, declaring that these Psalms reference the removal of Judas as an apostle (Psalms 69:25, Psalms 109:). Judas' homestead is indeed now desolate—he is dead—but another man must take his office to do the work of the Lord as Christ's witness to all humans all over the world.

This might indicate that in addition to prayer, the disciples had spent time in the scriptures, with the new eyes to see and understand scripture that Jesus had given them. Jesus had opened the scriptures to them to allow them to see that they spoke of Him (Luke 24:45). In poring over the scriptures, they apparently came to the conclusion that it was prophesied that the Messiah would be betrayed, and that another disciple ought to take his place. They therefore concluded that they ought to act upon this prophecy.

Consistent with his role as the leader among the twelve, Peter stands and proposes that they take action.