Promise

Listen to Chapter 8 & 9
Read the "Promise"

... God continued, "My covenant is between me and you and every living thing with you. It is a covenant for all time to come. Here is the sign of the covenant I am making. I have put my rainbow in the clouds. It will be the sign of the covenant between me and the earth. Sometimes when I bring clouds over the earth, a rainbow will appear in them. Then I will remember my covenant between me and you and every kind of living thing. The waters will never become a flood to destroy all life again. ..." (New International Reader's Version)

The rainbow is a sign from God reminding us that he has promised never again to flood the entire earth destroying all life.