His name is an abbreviated form of Cleopatros, a common Hellenistic name meaning "son of a renowned father".
This occurs two days after the crucifixion, on the day of Jesus' resurrection. The two have heard the tomb of Jesus was found empty earlier that day. They are discussing the events of the past few days when a stranger asks them what they are discussing. "Their eyes were kept from recognizing him." He soon rebukes them for their unbelief and gives them a Bible study on prophecies about the Messiah. They ask the stranger to join them for the evening meal. When he breaks the bread "their eyes were opened" and they recognize him as the resurrected Jesus. Jesus immediately vanishes.
Cleopas and his friend hasten back to Jerusalem to carry the news to the other disciples, and learn Jesus has also appeared to them as well. A similar event is mentioned in the longer ending of Mark: the incident is without parallel in the gospels of Matthew and John.
Cleopas has no further occurrence in the New Testament, but in tradition he has often been identified with Clopas, another New Testament figure.