This is a reference to the biblical story of Noah and the ark. Noah sent a dove out from the ark to determine whether the flood waters sent by God to cover the world had abated yet. The dove returned with an olive branch, showing Noah that the water was receding:
Also he sent forth a dove from him, to see if the waters were abated from off the face of the ground;
But the dove found no rest for the sole of her foot, and she returned unto him into the ark, for the waters were on the face of the whole earth: then he put forth his hand, and took her, and pulled her in unto him into the ark.
And he stayed yet other seven days; and again he sent forth the dove out of the ark;
And the dove came in to him in the evening; and, lo, in her mouth was an olive leaf pluckt off: so Noah knew that the waters were abated from off the earth. (Genesis 8:8-12)