"Hi. I'm the guy who replaced Judas!" That might be the opening line for today's saint, because that was precisely who he was, the successor to Judas! Why did the apostles choose a successor to Judas? Because Jesus chose twelve apostles to represent the twelve tribes of Israel. The apostles were going to be the foundation for the New Israel, the new People of God, the members of the New Covenant. So when Judas committed suicide the apostles continued with the first example of apostolic succession.
Peter led the apostles after Jesus' ascension and said, "For it is written in the Book of Psalms: May another take his office. Therefore, it is necessary that one of the men who accompanied us the whole time the Lord Jesus came and went among us, beginning from the baptism of John until the day on which was was taken up from us, become with us a witness to his resurrection" (Acts 1: 20-22). So they chose Matthias from among two suggested. Thus, he became the next apostle.
Apostolic succession is crucial in our understanding of the authority of the Church. From the apostles came the Apostolic Fathers, men who were instrumental in spreading the faith, including bishops like Ignatius of Antioch, Polycarp, and Clement of Rome. After them came the Fathers of the Church for the first centuries, most of them bishops, like Irenaeus of Lyons, Ambrose of Milan, Athanasius of Alexandria, Basil of Caesarea, Augustine of Hippo, John Chrysostom, Gregory the Great, and more. These are not just names of dead men from long ago, but rather the patriarchs of the Church who handed down the faith they received from the apostles, like Matthias.