According to Genesis, the rainbow is the covenant sign mentioned after Noah leaves Noah’s Ark.
After Noah builds an altar and offers sacrifices, Genesis 9 describes God’s covenant with Noah and every living creature. God says the rainbow in the clouds will serve as the sign that the waters will not again become a flood destroying all life.
Several objects appear earlier in the story, including the dove and its olive leaf, but they are not covenant signs in Genesis. They function as indicators that the Flood waters are receding and that vegetation is returning. The altar belongs to Noah’s act of worship, not to the later sign itself.
The rainbow’s meaning is presented through remembrance: when it appears in the clouds, the covenant is recalled. Later cultural uses of the rainbow may add other meanings, but Genesis specifically links it to the post-Flood covenant.