Matthias was the thirteenth individual to become an Apostle, replacing Judas Iscariot after his betrayal of Jesus Christ and suicide. Matthias was the only Apostle not appointed directly by Jesus Himself, but was selected by the Apostles with a lot. Matthias status as an Apostle is controversial, given that Paul calls himself an Apostle; while Jesus did not appoint Matthias directly.
While little is known about Matthias, it is known he was present for all of Jesus's ministry: from his baptism by John the Baptist, to the Resurrection, and to the Ascension. Matthias was an eyewitness of these events and this would eventually lead to him being qualified for candidacy as an Apostle.
Selected as an Apostle
Matthias was among a group of about a hundred and twenty other believers, who were lead by the Apostles. Shortly after Jesus's ascension Matthias was gathered in the group of believers who were being addressed by Simon Peter. In Peter's speech he discussed how long ago David prophesied about the one who would become Judas. Peter quoted from the Book of Psalms the prophecy concerning Judas and a prophecy that they would need a replacement.
Matthias and a man named Barsabbas were nominated for to replace Judas. Matthias was nominated as a candidate, because he had been present for Jesus' ministry in its entirety. They all prayed for God's will in the selection, and then they cast lots to determine Judas's successor.The lots were casted and it landed on Matthias and so he was made an Apostle.
Difficulty as Apostle
Whether or not Matthias was truly able to be the replacement of Judas is often controversial. While there is no biblical explanation, or any indication his apostleship was invalid, Paul also refers to himself as an Apostle. Matthias is only Apostle who was not directly selected by Jesus Himself, while it seems that Paul considers himself an Apostle by the will of God. It is possible that Paul was a separate kind of Apostle, or was individually commissioned by Christ, independently.