Matthias was the apostle chosen by lot to replace Judas, so that the number of apostles remained twelve. We read of this in the Acts of the Apostles.

In those days Peter stood up among the brethren (the company of persons was in all about a hundred and twenty), and said, “Brethren, the scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David, concerning Judas who was guide to those who arrested Jesus. For he was numbered among us, and was allotted his share in this ministry. So one of the men who have accompanied us during all the time that the Lord Jesus went in and out among us, beginning from the baptism of John until the day when he was taken up from us — one of these men must become with us a witness to his resurrection.” And they put forward two, Joseph called Barsabbas, who was surnamed Justus, and Matthias. And they prayed and said, “Lord, who knowest the hearts of all men, show which one of these two thou hast chosen to take the place in this ministry and apostleship from which Judas turned aside, to go to his own place.” And they cast lots for them, and the lot fell on Matthias; and he was enrolled with the eleven apostles.
Acts 1:15-17,21-26

That is all that is written in Scripture on Matthias, although other sources (some of questionable reliability) tell of his ministry — allegedly in Judea, Cappadocia, Egypt and Ethiopia — and his eventual martyrdom — again, some sources say crucified, some say stoned to death at Colchis on the far eastern edge of the Black Sea.

He is customarily shown as bearing an axe; but again, there is no one interpretation to explain this symbolism.