After Saul is transformed by his encounter with Christ he begins proclaiming the good news of Jesus and eventually returns to Jerusalem.
But when he returns, the disciples are hesitant to accept him. It could be that they are still angry about how he helped rile up and cheer on the crowd as they stoned Stephen to death (Acts 7:59-8:1) or it could be that they were still afraid of him because of the threats and murder he breathed at them a short while ago (Acts 9:1).
Even though Barnabas was a friend of Stephen and even though he had been threatened by Paul’s rhetoric against the church, he was willing to take a chance to listen to Saul’s story.
The Bible doesn’t describe their encounter, but I can imagine Barnabas being led by the Spirit, going to Saul with an open heart and mind and listening deeply to his story.
Afterwards, Barnabas is the one who brings Saul to the apostles and tells them of the change Christ has wrought in Saul’s life.
This might be one of the greatest miracles God performs in the Book of Acts, enemies becoming friends by the power of Christ.