In the biblical Noah's Ark story, the rainbow is the sign of God's covenant after the Flood.
Genesis 9 says that God establishes a covenant with Noah, his descendants, and every living creature. The rainbow in the cloud serves as the visible sign of that covenant. When the rainbow appears, the text says it will remind God of the promise never again to destroy all life with a flood.
The covenant is broader than Noah's immediate family. Genesis explicitly includes future generations and the animals that survived the Flood. This makes the rainbow a sign associated with the whole living world in the story, not merely a private symbol for Noah.
The account does not present the rainbow as a new physical phenomenon. Instead, it gives the natural image a covenantal meaning within the narrative. In later art and popular culture, the rainbow often appears alongside the ark as a visual shorthand for the story's conclusion.