From the Treasury of Daily Prayer:

St. Barnabas was a Levite from Cyprus who sold some land and gave the proceeds to the early Christian community in Jerusalem (Acts 4:36-37). St. Paul informs us that he was a cousin of John Mark (Colossians 4:10). Barnabas was sent by the Jerusalem Church to oversee the young Church in Antioch (Acts 11:22). While there, he went to Tarsus and brought Paul back to Antioch to help him (Acts 11:25-26). It was this Church in Antioch that commissioned and sent Barnabas and Paul on the first missionary journey (Acts 13:2-3). When it was time for the second missionary journey, however, Barnabas and Paul disagreed about taking along John Mark. Barnabas took Mark and went to Cyprus; Paul took Silas and headed north through Syria and Cilicia (Acts 15:36-41). Nothing more is known of the activities of Barnabas, except that he was apparently known to the Corinthians (1 Corinthians 9:6). Tradition relates that Barnabas died a martyr’s death in Cyprus by being stoned.