The dove is a symbol of the Holy Spirit. It is taken from the story of Jesus' baptism, where the Spirit descended on him in the form of a dove. The three-rayed nimbus around its head identifies the Spirit as a member of the Trinity. A dove shown without the nimbus is a symbol of peace.

Matt. 3:16 As soon as Jesus was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and lighting on him. (NIV)