A common name meaning "Gift of God" or "From God Given", depending on who you ask. It began its popularity with the Jews soon after the Exile.
Matthew was actually born with the name Levi and was the son of Alphaeus. His profession before his discipling of Christ was a publican (a fancy name for tax collector) in the city of Capernaum.
Levi changed his name to 'Matthew' after one occasion when Jesus came up from the side of the lake, passed the custom-house where Matthew(Levi) was seated, and said to him, "Follow me." The Gospels say that Matthew arose and did follow him, and became his disciple (Matthew 9:9), and he changed his name to that which we know him by today, possibly in grateful memory of his call.
The evening of same day on which Jesus called him he held a "great feast", a farewell feast, to which he invited Jesus and his disciples, and probably many of old associates. Later, he was selected as one of the Jesus' twelve apostles.
His name doesn't occur again in the Gospel history except in the lists of the names of the apostles. The last notice of his name is in Acts 1:13. The time, place and manner of his death are unknown.