In heraldry these birds always seem to have a white tuft on their heads. Many heraldic symbols of doves include an olive branch in the bird's beak.
According to the biblical story, a dove was released by Noah after the flood to find land. It returned with an olive branch in its beak. This let Noah know that, somewhere, there had to be land. A dove with an olive branch has since become a symbol of peace.
The Holy Spirit
In Christian Iconography, a dove represents the Holy Spirit. This is in reference to Matthew 3:16 and Luke 3:22 where the Holy Spirit appeared as a dove at the Baptism of Jesus.
At Christian weddings, doves or other birds are released. This is a symbol of peace and tranquility in marriage.