The dove first appears carrying an olive leaf back to Noah's ark — the sign that the flood had receded and the earth was ready for a new beginning. Gentle and innocent (Jesus told his disciples to be harmless as doves), the dove became a natural picture of peace and purity, offered by the poor as a temple sacrifice.
Its greatest moment came at the Jordan, when the Spirit of God descended like a dove and lighted upon Jesus at his baptism. Ever since, the dove has been the church's image of the Holy Spirit — descending gently, bringing peace, hovering over new creation just as the Spirit hovered over the waters at the beginning. Where the dove rests, God is making something new.
The Dove in Scripture
And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: