What does Genesis 9:13 mean?

In the previous verse, God says there will be a sign of the new covenant promise He has made. God vowed to again never destroy the earth or wipe out all living things with a flood. Now He reveals that sign: the rainbow.

More specifically, God says that He has set His bow in the cloud. The word for bow can be used of a battle bow, but the description of the bow being set on the occasion of clouds and being visible on the earth—along with the fact that the same word can be used for rainbow—makes it clear God is speaking of the rainbow. This is a "sign" which people can see directly.

The language used by God here is meant to suggest the symbolic hanging up of a battle weapon after the war is done and it is time for peace. God is taking responsibility for creating rainbows as a symbol of His pledge to humanity and to animals, never again to send a global flood. While rainbows are a scientific, meteorological phenomenon, Genesis asserts that God is responsible for every scientific and meteorological phenomenon (Genesis 1:1; Psalm 19:1). God chose to cause rainbows to function as a symbol of His covenant promise.