From the Treasury of Daily Prayer:

St. Mark was the author of the second Gospel, which he composed, according to some Early Church Fathers, when the Christians in Rome asked him to write down the preaching of the apostle Peter. Mark, also known as John Mark, was originally from Jerusalem, where the house of his mother Mary was the center of the early Jerusalem Church (Acts 12:12). He was brought from Jerusalem by Paul and Barnabas to Antioch (Acts 12:25), and it was from this city that they set out on the first missionary journey. When Paul and Barnabas were preparing to go on the second missionary journey, Barnabas wanted to take Mark with them again, but Paul objected because Mark had left them during the first journey. Barnabas took Mark and went to Cyprus, while Paul took Silas as his new companion (Acts 15:37-40). Later, Paul reconciled with Mark and was working with him again (Colossians 4:10; Philemon 24; 2 Timothy 4:11). Finally, Mark was found laboring with Peter in Rome (1 Peter 5:13). Tradition says that Mark was instrumental in founding the Church in Alexandria, becoming its first bishop, and also that he suffered a martyr’s death.