Genesis 9: 12-13 "And God said, 'This is the sign of the covenant which I make between me and you and every living creature that is with you, for all future generations; I set my bow in the cloud, and it shall be a sign of the covenant between me and the earth.'"
At the time of Noah, the wickedness of man had become very great, and it grieved God, so that He determined to send a great flood to destroy the earth. And yet again, he provided salvation by way of Noah and the ark. New life came after the flood, and the rainbow remains the sign of God's covenant promise.